Modeling Capital Markets with
Financial Signal processing
Bridging Technical Analysis amp Stochastic-Process Modeling
( I )
Harmonic Financial Engineering
調和財務工程部 騰網知識科技開發
a step toward
Rational Memory ProcessCanonical Foundation of Financial Engineering by Sifeon
Capturing Movements of
Capital Markets
Dynamics of Time-Series Fluctuation to determine Growth Path
Example SampP 500 Index (US Stock Market)
Time Series of Monthly Return Rates
Dynamic Analysis of
Market Movements
various approaches from different perspectives and for different purposes
Categories of Analyzing Methodologies
Technical Analysis Stochastic-Process Modeling
Fundamental Analysis Inter-Market Analysis
Endogenous
ExogenousTraditional
Financial AnalysisAdvanced
Financial Engineering
Demand-Supply Mechanism
Growth-Value Perspective
Return-Risk Trade-off
Dynamics of Capital Flows
Part I
Elementary Ideas in
Technical Analysis
naiumlve financial signal processing
Reading Charts of
Market Movements
Technical Analysis ( 技術分析 ) = 看圖說故事
Correction ( 振盪整理 )
Uncertainty
Momentum
Finding Technical Patterns of
Market Demand-Supply
Momentum Risk Aversion and Bargain
Technical Analysis as
Financial Signal Processing
consistent Cycle-Leading Patterns out there
FilterEndogenousMarket Data Indicator
Market-CycleLeading PatternHistoric SimulationEmpirical
Strategy
fitting into noisesor
figuring out trendsor
creating cycles
bull Strength ndash Observation amp Explanation about Dynamic Phenomena
trying to explain filtered patterns based on
market demand-supply mechanism driven by market sentiment
eg
Moving Average (EMA MACD) Relative Strength Index Money Flow IndexBollinger Bands Support and Resistance Levels
bull Weakness ndash Formulation amp Correction about Dynamic Structure
lack of probabilistic formulation for
consistent strategy construction by risk-return trade-off and
systematic performance assessment
Strength and Weakness of
Technical Analysis
be aware of noisy illusions
Part II
Fundamental Structures in
Stochastic-Process Modeling
naiumlve capital market modeling
recognizing the random nature and formalizing the stochastic structure
Time Series of Periodic Return Rates
Mathematical Foundation of
Financial Engineering
Ri = (Si-Si-1)Si-1
Probabilistic Formulation L(Rii=1 hellip) ndash Joint Distribution
Dynamic Statistics Lθ(i) (Ri)i=1 hellip ndash Stochastic Evolution
Information Implication L(Si+1|Si)i=1 hellip ndash Prob Transition
Academic Canonical Frameworks of
Capital Market Modeling
Discrete-Time Version
(Auto-Regression)
Continuous-Time Version
(Stochastic Differential Equation)
IID Normal Sequence Geometric Brownian Motion
Ri = μ+σεi εi ~ N(01) dStSt = rmiddotdt + smiddotdWt
GARCH SVM (Mean-Reverting Process)
Ri = μ+σiεi εi ~ N(01)
σi 2 = α0+Σp
j=1αj εi-j2 +Σq
j=1βj σ i-j2
dStSt = rmiddotdt + |Vt|middotdWt
dVt = -kmiddot(Vt-c)middotdt + f(Vt)dZt
Generalization Generalization
Ri = μ(Ri-1 Ri-2 hellip)+σ (Ri-1 Ri-2 hellip) εi dStSt = Mtmiddotdt + VtmiddotdWt
could the models borrowed from physical systems well approach econ ones
Finding Clues for
Verifying Models
just simply a normal distributionor
a complicated mixture of normal distributions
tractable Dynamic Structure out there
dynamic tracingstatic de-mixing
bull Strength ndash Formulation amp Correction about Dynamic Structure
strong probabilistic formulation for
consistent strategy construction by risk-return trade-off and
systematic risk management (tools amp paradigms by financial engineering)
bull Weakness ndash Observation amp Explanation about Dynamic Phenomena
Ignoring (if any) ldquocyclic phenomenardquo and ldquoinvestment paradigmsrdquodue to
market demand-supply mechanism driven by
market sentiment and rationality
Strength and Weakness of
Stochastic-Process Modeling
be aware of simple biases
Part III
Reality amp
Lessons
itrsquos a jungle out there
bull Capital Markets are Complex Dynamic Systemsbull Non-linear Dynamic Mechanismbull Non-stationary Evolution due to changing Econ Conditions and Investment Paradigms
bull Multi-Component Framework of Market Behaviorbull Trend ndash Change Points Long-Term Evolutionary Structural Changesbull Seasonality ndash Periodic Factors bull Cycles ndash Dynamic Swings around Equilibriumbull Shocks ndash Unpredictable Impactsbull Noises ndash Endogenous and Environmental Uncertainties
bull Diversification in Market Constitutionbull Sentiment ndash Individual Investorsbull Rationality ndash Institutional Investors (Smart Money)bull Strategy ndash Arbitrageurs Risk Hedgers
bull Multi-Channel Infrastructure of Money Flowsbull Swifter and Swifter Trading Systemsbull Broader and Broader Asset Categoriesbull More Sophisticated and Complicated Financial Products and Trading Schemes
bull Reflexivity
The Complex Reality for
Thoughts
too many factors affecting market movements to figure out
can
deal with it
GARCH
Multi-Resolutionof
Complex Market Time Series
wavelet-based decomposition to figure out market behavior features
1974 Great Stock Market Capitulation
1987 Great Stock Market Crash
1989 Nikkei Bubble Burst
1997 Asian Currency Crisis
1998 LTCM Fallout
2000 Nasdaq (Tech) Bubble Burst
Hard Lessons from
Markets
dynamic risks beyond interpretation of stochastic volatility (no anomaly talk)
Part IV
Rational Memory Processes
a canonical methodological frameworkof
capital market modeling based on
financial signal processing
bull Theoretical Issues (about mathematical analysis)bull Dynamics ndash Demand Supply Mechanism
bull Randomness ndash Uncertainty Structure (multi-scale noise structure)
bull Practical Issues (about paradigms)bull Market Sentiment ndash Momentum Uncertainty
bull Market Rationality ndash Prediction Risk-Return Trade-Off
bull Market Strategy ndash Arbitrage Risk Hedging Schemes
bull Market Efficiency amp Completeness ndash Financial Infrastructures Products
bull Market Liquidity amp Friction ndash Trading Volumes Cost Turn-Over rate
bull Market Constitution ndash Economical Cultural Geopolitical Backgrounds
bull Technical Issues (about applications and implications)bull Model Identification ndash Parameter Estimation
bull Model Assessment ndash Modeling Risk (Modeling Bias Estimation Loss)
bull Model Adaptation ndash Coefficient Relations to Econ and Other Marketsrsquo Conditions
bull Model Extensibility ndash Extension to Absorb New Factors counting for ldquoAnomaliesrdquo
Prospects for
Modeling Capital Markets
setting a modeling methodological framework to incorporate the prospects
Challenges for
Modeling Capital Markets
bull Non-linearity amp Non-stationarity in Signal Dynamics
bull Complexity in Signal Structure
bull Noise Barrier (Overwhelming Noise-to-Signal Ratio)
bull Nonparametric Estimation (MLE does not make sense anymore here)
Curse of Dimensionality
1 2 3 4 5 6 7 8 9 10 11 12
Piecewise (Monthly) Constant Geometric Brownian Motion
Ri = μ(Ri-1 Ri-2 hellip)+σ (Ri-1 Ri-2 hellip) εi
Technical Foundationfor
Financial Signal Processing
Transformation Magic to break Curse of Dimensionality
Analyzing Signals over Fourier Frequency Domain
Analyzing Signals in Wavelet Multi-Resolution Framework
Complexity in Signal Structure
Non-linearity amp Non-stationarity in Signal Dynamics
Analyzing Signals over Dynamic Domain
in
Wavelet Multi-Resolution Framework
Fundamental Signal Processing Tasksfor
Financial Engineering
an objective way to format market patterns from experience
FilterHistoric
Time SeriesTechnicalIndicator
DiS0 S1 hellip Si
Di =Г(S0 hellip Si V0 hellip Vi |өi)
Dt =Гt(Sτ[0t])continuous-time approach
special interested format
Di =Г(R1 hellip Ri) Rj = (Sj-Sj-1)Sj-1
linear stationary case
Di = c1middotR1 + hellip + cimiddotRi Dt = int[0t]k(|τ-t|)middotSτ-1dSτ
Examples of
Dynamic Indicators
Dancing with Cycles
0 100 200 300 400 500 600 700-5
-4
-3
-2
-1
0
1
2
3
4
5
121951 022003
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
Dynamic Indicators Technical Indicators which serve to monitor and gauge market cycles
Critical Patternsof
Long-Term Cyclic Phenomena
0 50 100 150-2
-1
0
1
2
3
4
Jul 1993
Oct 1987
Nov 1981
Feb 1986
MaxUncertaintyLine
12-Month STTB Moving Average 12-Month SampP500 Return MA ()
Principle of Cyclic Hazard
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
1285 1290 0496
0401
Nikkei 225 SampP 500
TAIEX
Example Iof
Short-Horizon Dynamic Patterns
catching rebounding points and finding implicit trend forces
Fidelity Emerging Markets Fund (USD)
Fidelity Technology Fund (EUR) Fidelity American Growth Fund (USD)
Fidelity World Fund (EUR)
08182003 0120204 08182003 0120204
08182003 0120204 08182003 0120204
Index Value
20-Day STTB
Example IIof
Short-Horizon Dynamic Patterns
catching a rebounding and surging point
20-Day STTB
Example IIIof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Currency Triangular Arbitraging
12-Month MA of USD-vs-EUR Return Rate
12-Month MA of USD-vs-JPY Return Rate
12-Month MA of USD-vs-EUR 12-M STTB
12-Month MA of USD-vs-JPY 12-M STTB
Example IVof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Stock-Index Triangular Arbitraging
02132003 01162004
TWSEBKITWSE Cumulative Relative Return Rate (3)
TWSEELECTWSE Cumulative Relative Return Rate (3)
5-Day MA of TWSEBKITWSE Relative 20-Day STTB
5-Day MA of TWSEELECTWSE Relative 20-Day STTB
bull Physical Meanings - indicating practical market sense eg momentum uncertainty stability liquidity hellip etc
bull Cycle-Leading
bull Consistency amp Universality (Time amp Geography)
Conditionsof
Modeling Potential
warning markets might have no real intentions but filtersrsquo illusions
0 10 20 30 40 50 60-2
-1
0
1
2
3
4
011981 061985
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
- eg
Constructing Indicator-Oriented Strategieswith or without
Modeling
from empirical to theoretical
0 05 1 15 2 25 3 35 4-2
0
2
4
6
8
10H i+1
Si
Empirical Raw Optimal Strategy Theoretical Raw Optimal Strategy ΨΣ2
Methodological Framework of
Modeling Capital Markets
dynamics based on rationality oriented by memory filtered by dynamic kernel
Rational Memory Process
Ri+1-ri = Ψө(Di) + Ση(Di)middotεi+1
continuous-time approach (with a linear stationary filter)
dStSt = Ψө(int[0t]k(|τ-t|)middotSτ-1dSτ) middotdt + Ση(int[0t]k(|τ-t|)middotSτ
-1dSτ)middotdWt
Market Aggregation Rationality
Market Background Conditions
bull neatly constructing dynamic investment strategies on the dynamic domain
bull analytic calculation of risk-return trade-off curve via calculus of variation
bull easily formulating integrated-volatility for simulating risk-neutral probability density and calculating VaR
bull turning nonlinear dynamic auto-regression into static nonparametric regression
bull introducing adaptive statistical estimation methods to separate stationary and non-stationary factors
bull assessing modeling risk
bull paving a way to ldquostatistical financerdquo (market energy)
bull keeping the modeling framework flexible and adaptive under reflexivity
bull pricing profitable financial knowledges based on valuable dynamic kernels
Advantages on
Dynamic Domain
building robust amp adaptive models for financial engineering in magic domains
a step toward
Rational Memory ProcessCanonical Foundation of Financial Engineering by Sifeon
Capturing Movements of
Capital Markets
Dynamics of Time-Series Fluctuation to determine Growth Path
Example SampP 500 Index (US Stock Market)
Time Series of Monthly Return Rates
Dynamic Analysis of
Market Movements
various approaches from different perspectives and for different purposes
Categories of Analyzing Methodologies
Technical Analysis Stochastic-Process Modeling
Fundamental Analysis Inter-Market Analysis
Endogenous
ExogenousTraditional
Financial AnalysisAdvanced
Financial Engineering
Demand-Supply Mechanism
Growth-Value Perspective
Return-Risk Trade-off
Dynamics of Capital Flows
Part I
Elementary Ideas in
Technical Analysis
naiumlve financial signal processing
Reading Charts of
Market Movements
Technical Analysis ( 技術分析 ) = 看圖說故事
Correction ( 振盪整理 )
Uncertainty
Momentum
Finding Technical Patterns of
Market Demand-Supply
Momentum Risk Aversion and Bargain
Technical Analysis as
Financial Signal Processing
consistent Cycle-Leading Patterns out there
FilterEndogenousMarket Data Indicator
Market-CycleLeading PatternHistoric SimulationEmpirical
Strategy
fitting into noisesor
figuring out trendsor
creating cycles
bull Strength ndash Observation amp Explanation about Dynamic Phenomena
trying to explain filtered patterns based on
market demand-supply mechanism driven by market sentiment
eg
Moving Average (EMA MACD) Relative Strength Index Money Flow IndexBollinger Bands Support and Resistance Levels
bull Weakness ndash Formulation amp Correction about Dynamic Structure
lack of probabilistic formulation for
consistent strategy construction by risk-return trade-off and
systematic performance assessment
Strength and Weakness of
Technical Analysis
be aware of noisy illusions
Part II
Fundamental Structures in
Stochastic-Process Modeling
naiumlve capital market modeling
recognizing the random nature and formalizing the stochastic structure
Time Series of Periodic Return Rates
Mathematical Foundation of
Financial Engineering
Ri = (Si-Si-1)Si-1
Probabilistic Formulation L(Rii=1 hellip) ndash Joint Distribution
Dynamic Statistics Lθ(i) (Ri)i=1 hellip ndash Stochastic Evolution
Information Implication L(Si+1|Si)i=1 hellip ndash Prob Transition
Academic Canonical Frameworks of
Capital Market Modeling
Discrete-Time Version
(Auto-Regression)
Continuous-Time Version
(Stochastic Differential Equation)
IID Normal Sequence Geometric Brownian Motion
Ri = μ+σεi εi ~ N(01) dStSt = rmiddotdt + smiddotdWt
GARCH SVM (Mean-Reverting Process)
Ri = μ+σiεi εi ~ N(01)
σi 2 = α0+Σp
j=1αj εi-j2 +Σq
j=1βj σ i-j2
dStSt = rmiddotdt + |Vt|middotdWt
dVt = -kmiddot(Vt-c)middotdt + f(Vt)dZt
Generalization Generalization
Ri = μ(Ri-1 Ri-2 hellip)+σ (Ri-1 Ri-2 hellip) εi dStSt = Mtmiddotdt + VtmiddotdWt
could the models borrowed from physical systems well approach econ ones
Finding Clues for
Verifying Models
just simply a normal distributionor
a complicated mixture of normal distributions
tractable Dynamic Structure out there
dynamic tracingstatic de-mixing
bull Strength ndash Formulation amp Correction about Dynamic Structure
strong probabilistic formulation for
consistent strategy construction by risk-return trade-off and
systematic risk management (tools amp paradigms by financial engineering)
bull Weakness ndash Observation amp Explanation about Dynamic Phenomena
Ignoring (if any) ldquocyclic phenomenardquo and ldquoinvestment paradigmsrdquodue to
market demand-supply mechanism driven by
market sentiment and rationality
Strength and Weakness of
Stochastic-Process Modeling
be aware of simple biases
Part III
Reality amp
Lessons
itrsquos a jungle out there
bull Capital Markets are Complex Dynamic Systemsbull Non-linear Dynamic Mechanismbull Non-stationary Evolution due to changing Econ Conditions and Investment Paradigms
bull Multi-Component Framework of Market Behaviorbull Trend ndash Change Points Long-Term Evolutionary Structural Changesbull Seasonality ndash Periodic Factors bull Cycles ndash Dynamic Swings around Equilibriumbull Shocks ndash Unpredictable Impactsbull Noises ndash Endogenous and Environmental Uncertainties
bull Diversification in Market Constitutionbull Sentiment ndash Individual Investorsbull Rationality ndash Institutional Investors (Smart Money)bull Strategy ndash Arbitrageurs Risk Hedgers
bull Multi-Channel Infrastructure of Money Flowsbull Swifter and Swifter Trading Systemsbull Broader and Broader Asset Categoriesbull More Sophisticated and Complicated Financial Products and Trading Schemes
bull Reflexivity
The Complex Reality for
Thoughts
too many factors affecting market movements to figure out
can
deal with it
GARCH
Multi-Resolutionof
Complex Market Time Series
wavelet-based decomposition to figure out market behavior features
1974 Great Stock Market Capitulation
1987 Great Stock Market Crash
1989 Nikkei Bubble Burst
1997 Asian Currency Crisis
1998 LTCM Fallout
2000 Nasdaq (Tech) Bubble Burst
Hard Lessons from
Markets
dynamic risks beyond interpretation of stochastic volatility (no anomaly talk)
Part IV
Rational Memory Processes
a canonical methodological frameworkof
capital market modeling based on
financial signal processing
bull Theoretical Issues (about mathematical analysis)bull Dynamics ndash Demand Supply Mechanism
bull Randomness ndash Uncertainty Structure (multi-scale noise structure)
bull Practical Issues (about paradigms)bull Market Sentiment ndash Momentum Uncertainty
bull Market Rationality ndash Prediction Risk-Return Trade-Off
bull Market Strategy ndash Arbitrage Risk Hedging Schemes
bull Market Efficiency amp Completeness ndash Financial Infrastructures Products
bull Market Liquidity amp Friction ndash Trading Volumes Cost Turn-Over rate
bull Market Constitution ndash Economical Cultural Geopolitical Backgrounds
bull Technical Issues (about applications and implications)bull Model Identification ndash Parameter Estimation
bull Model Assessment ndash Modeling Risk (Modeling Bias Estimation Loss)
bull Model Adaptation ndash Coefficient Relations to Econ and Other Marketsrsquo Conditions
bull Model Extensibility ndash Extension to Absorb New Factors counting for ldquoAnomaliesrdquo
Prospects for
Modeling Capital Markets
setting a modeling methodological framework to incorporate the prospects
Challenges for
Modeling Capital Markets
bull Non-linearity amp Non-stationarity in Signal Dynamics
bull Complexity in Signal Structure
bull Noise Barrier (Overwhelming Noise-to-Signal Ratio)
bull Nonparametric Estimation (MLE does not make sense anymore here)
Curse of Dimensionality
1 2 3 4 5 6 7 8 9 10 11 12
Piecewise (Monthly) Constant Geometric Brownian Motion
Ri = μ(Ri-1 Ri-2 hellip)+σ (Ri-1 Ri-2 hellip) εi
Technical Foundationfor
Financial Signal Processing
Transformation Magic to break Curse of Dimensionality
Analyzing Signals over Fourier Frequency Domain
Analyzing Signals in Wavelet Multi-Resolution Framework
Complexity in Signal Structure
Non-linearity amp Non-stationarity in Signal Dynamics
Analyzing Signals over Dynamic Domain
in
Wavelet Multi-Resolution Framework
Fundamental Signal Processing Tasksfor
Financial Engineering
an objective way to format market patterns from experience
FilterHistoric
Time SeriesTechnicalIndicator
DiS0 S1 hellip Si
Di =Г(S0 hellip Si V0 hellip Vi |өi)
Dt =Гt(Sτ[0t])continuous-time approach
special interested format
Di =Г(R1 hellip Ri) Rj = (Sj-Sj-1)Sj-1
linear stationary case
Di = c1middotR1 + hellip + cimiddotRi Dt = int[0t]k(|τ-t|)middotSτ-1dSτ
Examples of
Dynamic Indicators
Dancing with Cycles
0 100 200 300 400 500 600 700-5
-4
-3
-2
-1
0
1
2
3
4
5
121951 022003
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
Dynamic Indicators Technical Indicators which serve to monitor and gauge market cycles
Critical Patternsof
Long-Term Cyclic Phenomena
0 50 100 150-2
-1
0
1
2
3
4
Jul 1993
Oct 1987
Nov 1981
Feb 1986
MaxUncertaintyLine
12-Month STTB Moving Average 12-Month SampP500 Return MA ()
Principle of Cyclic Hazard
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
1285 1290 0496
0401
Nikkei 225 SampP 500
TAIEX
Example Iof
Short-Horizon Dynamic Patterns
catching rebounding points and finding implicit trend forces
Fidelity Emerging Markets Fund (USD)
Fidelity Technology Fund (EUR) Fidelity American Growth Fund (USD)
Fidelity World Fund (EUR)
08182003 0120204 08182003 0120204
08182003 0120204 08182003 0120204
Index Value
20-Day STTB
Example IIof
Short-Horizon Dynamic Patterns
catching a rebounding and surging point
20-Day STTB
Example IIIof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Currency Triangular Arbitraging
12-Month MA of USD-vs-EUR Return Rate
12-Month MA of USD-vs-JPY Return Rate
12-Month MA of USD-vs-EUR 12-M STTB
12-Month MA of USD-vs-JPY 12-M STTB
Example IVof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Stock-Index Triangular Arbitraging
02132003 01162004
TWSEBKITWSE Cumulative Relative Return Rate (3)
TWSEELECTWSE Cumulative Relative Return Rate (3)
5-Day MA of TWSEBKITWSE Relative 20-Day STTB
5-Day MA of TWSEELECTWSE Relative 20-Day STTB
bull Physical Meanings - indicating practical market sense eg momentum uncertainty stability liquidity hellip etc
bull Cycle-Leading
bull Consistency amp Universality (Time amp Geography)
Conditionsof
Modeling Potential
warning markets might have no real intentions but filtersrsquo illusions
0 10 20 30 40 50 60-2
-1
0
1
2
3
4
011981 061985
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
- eg
Constructing Indicator-Oriented Strategieswith or without
Modeling
from empirical to theoretical
0 05 1 15 2 25 3 35 4-2
0
2
4
6
8
10H i+1
Si
Empirical Raw Optimal Strategy Theoretical Raw Optimal Strategy ΨΣ2
Methodological Framework of
Modeling Capital Markets
dynamics based on rationality oriented by memory filtered by dynamic kernel
Rational Memory Process
Ri+1-ri = Ψө(Di) + Ση(Di)middotεi+1
continuous-time approach (with a linear stationary filter)
dStSt = Ψө(int[0t]k(|τ-t|)middotSτ-1dSτ) middotdt + Ση(int[0t]k(|τ-t|)middotSτ
-1dSτ)middotdWt
Market Aggregation Rationality
Market Background Conditions
bull neatly constructing dynamic investment strategies on the dynamic domain
bull analytic calculation of risk-return trade-off curve via calculus of variation
bull easily formulating integrated-volatility for simulating risk-neutral probability density and calculating VaR
bull turning nonlinear dynamic auto-regression into static nonparametric regression
bull introducing adaptive statistical estimation methods to separate stationary and non-stationary factors
bull assessing modeling risk
bull paving a way to ldquostatistical financerdquo (market energy)
bull keeping the modeling framework flexible and adaptive under reflexivity
bull pricing profitable financial knowledges based on valuable dynamic kernels
Advantages on
Dynamic Domain
building robust amp adaptive models for financial engineering in magic domains
Capturing Movements of
Capital Markets
Dynamics of Time-Series Fluctuation to determine Growth Path
Example SampP 500 Index (US Stock Market)
Time Series of Monthly Return Rates
Dynamic Analysis of
Market Movements
various approaches from different perspectives and for different purposes
Categories of Analyzing Methodologies
Technical Analysis Stochastic-Process Modeling
Fundamental Analysis Inter-Market Analysis
Endogenous
ExogenousTraditional
Financial AnalysisAdvanced
Financial Engineering
Demand-Supply Mechanism
Growth-Value Perspective
Return-Risk Trade-off
Dynamics of Capital Flows
Part I
Elementary Ideas in
Technical Analysis
naiumlve financial signal processing
Reading Charts of
Market Movements
Technical Analysis ( 技術分析 ) = 看圖說故事
Correction ( 振盪整理 )
Uncertainty
Momentum
Finding Technical Patterns of
Market Demand-Supply
Momentum Risk Aversion and Bargain
Technical Analysis as
Financial Signal Processing
consistent Cycle-Leading Patterns out there
FilterEndogenousMarket Data Indicator
Market-CycleLeading PatternHistoric SimulationEmpirical
Strategy
fitting into noisesor
figuring out trendsor
creating cycles
bull Strength ndash Observation amp Explanation about Dynamic Phenomena
trying to explain filtered patterns based on
market demand-supply mechanism driven by market sentiment
eg
Moving Average (EMA MACD) Relative Strength Index Money Flow IndexBollinger Bands Support and Resistance Levels
bull Weakness ndash Formulation amp Correction about Dynamic Structure
lack of probabilistic formulation for
consistent strategy construction by risk-return trade-off and
systematic performance assessment
Strength and Weakness of
Technical Analysis
be aware of noisy illusions
Part II
Fundamental Structures in
Stochastic-Process Modeling
naiumlve capital market modeling
recognizing the random nature and formalizing the stochastic structure
Time Series of Periodic Return Rates
Mathematical Foundation of
Financial Engineering
Ri = (Si-Si-1)Si-1
Probabilistic Formulation L(Rii=1 hellip) ndash Joint Distribution
Dynamic Statistics Lθ(i) (Ri)i=1 hellip ndash Stochastic Evolution
Information Implication L(Si+1|Si)i=1 hellip ndash Prob Transition
Academic Canonical Frameworks of
Capital Market Modeling
Discrete-Time Version
(Auto-Regression)
Continuous-Time Version
(Stochastic Differential Equation)
IID Normal Sequence Geometric Brownian Motion
Ri = μ+σεi εi ~ N(01) dStSt = rmiddotdt + smiddotdWt
GARCH SVM (Mean-Reverting Process)
Ri = μ+σiεi εi ~ N(01)
σi 2 = α0+Σp
j=1αj εi-j2 +Σq
j=1βj σ i-j2
dStSt = rmiddotdt + |Vt|middotdWt
dVt = -kmiddot(Vt-c)middotdt + f(Vt)dZt
Generalization Generalization
Ri = μ(Ri-1 Ri-2 hellip)+σ (Ri-1 Ri-2 hellip) εi dStSt = Mtmiddotdt + VtmiddotdWt
could the models borrowed from physical systems well approach econ ones
Finding Clues for
Verifying Models
just simply a normal distributionor
a complicated mixture of normal distributions
tractable Dynamic Structure out there
dynamic tracingstatic de-mixing
bull Strength ndash Formulation amp Correction about Dynamic Structure
strong probabilistic formulation for
consistent strategy construction by risk-return trade-off and
systematic risk management (tools amp paradigms by financial engineering)
bull Weakness ndash Observation amp Explanation about Dynamic Phenomena
Ignoring (if any) ldquocyclic phenomenardquo and ldquoinvestment paradigmsrdquodue to
market demand-supply mechanism driven by
market sentiment and rationality
Strength and Weakness of
Stochastic-Process Modeling
be aware of simple biases
Part III
Reality amp
Lessons
itrsquos a jungle out there
bull Capital Markets are Complex Dynamic Systemsbull Non-linear Dynamic Mechanismbull Non-stationary Evolution due to changing Econ Conditions and Investment Paradigms
bull Multi-Component Framework of Market Behaviorbull Trend ndash Change Points Long-Term Evolutionary Structural Changesbull Seasonality ndash Periodic Factors bull Cycles ndash Dynamic Swings around Equilibriumbull Shocks ndash Unpredictable Impactsbull Noises ndash Endogenous and Environmental Uncertainties
bull Diversification in Market Constitutionbull Sentiment ndash Individual Investorsbull Rationality ndash Institutional Investors (Smart Money)bull Strategy ndash Arbitrageurs Risk Hedgers
bull Multi-Channel Infrastructure of Money Flowsbull Swifter and Swifter Trading Systemsbull Broader and Broader Asset Categoriesbull More Sophisticated and Complicated Financial Products and Trading Schemes
bull Reflexivity
The Complex Reality for
Thoughts
too many factors affecting market movements to figure out
can
deal with it
GARCH
Multi-Resolutionof
Complex Market Time Series
wavelet-based decomposition to figure out market behavior features
1974 Great Stock Market Capitulation
1987 Great Stock Market Crash
1989 Nikkei Bubble Burst
1997 Asian Currency Crisis
1998 LTCM Fallout
2000 Nasdaq (Tech) Bubble Burst
Hard Lessons from
Markets
dynamic risks beyond interpretation of stochastic volatility (no anomaly talk)
Part IV
Rational Memory Processes
a canonical methodological frameworkof
capital market modeling based on
financial signal processing
bull Theoretical Issues (about mathematical analysis)bull Dynamics ndash Demand Supply Mechanism
bull Randomness ndash Uncertainty Structure (multi-scale noise structure)
bull Practical Issues (about paradigms)bull Market Sentiment ndash Momentum Uncertainty
bull Market Rationality ndash Prediction Risk-Return Trade-Off
bull Market Strategy ndash Arbitrage Risk Hedging Schemes
bull Market Efficiency amp Completeness ndash Financial Infrastructures Products
bull Market Liquidity amp Friction ndash Trading Volumes Cost Turn-Over rate
bull Market Constitution ndash Economical Cultural Geopolitical Backgrounds
bull Technical Issues (about applications and implications)bull Model Identification ndash Parameter Estimation
bull Model Assessment ndash Modeling Risk (Modeling Bias Estimation Loss)
bull Model Adaptation ndash Coefficient Relations to Econ and Other Marketsrsquo Conditions
bull Model Extensibility ndash Extension to Absorb New Factors counting for ldquoAnomaliesrdquo
Prospects for
Modeling Capital Markets
setting a modeling methodological framework to incorporate the prospects
Challenges for
Modeling Capital Markets
bull Non-linearity amp Non-stationarity in Signal Dynamics
bull Complexity in Signal Structure
bull Noise Barrier (Overwhelming Noise-to-Signal Ratio)
bull Nonparametric Estimation (MLE does not make sense anymore here)
Curse of Dimensionality
1 2 3 4 5 6 7 8 9 10 11 12
Piecewise (Monthly) Constant Geometric Brownian Motion
Ri = μ(Ri-1 Ri-2 hellip)+σ (Ri-1 Ri-2 hellip) εi
Technical Foundationfor
Financial Signal Processing
Transformation Magic to break Curse of Dimensionality
Analyzing Signals over Fourier Frequency Domain
Analyzing Signals in Wavelet Multi-Resolution Framework
Complexity in Signal Structure
Non-linearity amp Non-stationarity in Signal Dynamics
Analyzing Signals over Dynamic Domain
in
Wavelet Multi-Resolution Framework
Fundamental Signal Processing Tasksfor
Financial Engineering
an objective way to format market patterns from experience
FilterHistoric
Time SeriesTechnicalIndicator
DiS0 S1 hellip Si
Di =Г(S0 hellip Si V0 hellip Vi |өi)
Dt =Гt(Sτ[0t])continuous-time approach
special interested format
Di =Г(R1 hellip Ri) Rj = (Sj-Sj-1)Sj-1
linear stationary case
Di = c1middotR1 + hellip + cimiddotRi Dt = int[0t]k(|τ-t|)middotSτ-1dSτ
Examples of
Dynamic Indicators
Dancing with Cycles
0 100 200 300 400 500 600 700-5
-4
-3
-2
-1
0
1
2
3
4
5
121951 022003
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
Dynamic Indicators Technical Indicators which serve to monitor and gauge market cycles
Critical Patternsof
Long-Term Cyclic Phenomena
0 50 100 150-2
-1
0
1
2
3
4
Jul 1993
Oct 1987
Nov 1981
Feb 1986
MaxUncertaintyLine
12-Month STTB Moving Average 12-Month SampP500 Return MA ()
Principle of Cyclic Hazard
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
1285 1290 0496
0401
Nikkei 225 SampP 500
TAIEX
Example Iof
Short-Horizon Dynamic Patterns
catching rebounding points and finding implicit trend forces
Fidelity Emerging Markets Fund (USD)
Fidelity Technology Fund (EUR) Fidelity American Growth Fund (USD)
Fidelity World Fund (EUR)
08182003 0120204 08182003 0120204
08182003 0120204 08182003 0120204
Index Value
20-Day STTB
Example IIof
Short-Horizon Dynamic Patterns
catching a rebounding and surging point
20-Day STTB
Example IIIof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Currency Triangular Arbitraging
12-Month MA of USD-vs-EUR Return Rate
12-Month MA of USD-vs-JPY Return Rate
12-Month MA of USD-vs-EUR 12-M STTB
12-Month MA of USD-vs-JPY 12-M STTB
Example IVof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Stock-Index Triangular Arbitraging
02132003 01162004
TWSEBKITWSE Cumulative Relative Return Rate (3)
TWSEELECTWSE Cumulative Relative Return Rate (3)
5-Day MA of TWSEBKITWSE Relative 20-Day STTB
5-Day MA of TWSEELECTWSE Relative 20-Day STTB
bull Physical Meanings - indicating practical market sense eg momentum uncertainty stability liquidity hellip etc
bull Cycle-Leading
bull Consistency amp Universality (Time amp Geography)
Conditionsof
Modeling Potential
warning markets might have no real intentions but filtersrsquo illusions
0 10 20 30 40 50 60-2
-1
0
1
2
3
4
011981 061985
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
- eg
Constructing Indicator-Oriented Strategieswith or without
Modeling
from empirical to theoretical
0 05 1 15 2 25 3 35 4-2
0
2
4
6
8
10H i+1
Si
Empirical Raw Optimal Strategy Theoretical Raw Optimal Strategy ΨΣ2
Methodological Framework of
Modeling Capital Markets
dynamics based on rationality oriented by memory filtered by dynamic kernel
Rational Memory Process
Ri+1-ri = Ψө(Di) + Ση(Di)middotεi+1
continuous-time approach (with a linear stationary filter)
dStSt = Ψө(int[0t]k(|τ-t|)middotSτ-1dSτ) middotdt + Ση(int[0t]k(|τ-t|)middotSτ
-1dSτ)middotdWt
Market Aggregation Rationality
Market Background Conditions
bull neatly constructing dynamic investment strategies on the dynamic domain
bull analytic calculation of risk-return trade-off curve via calculus of variation
bull easily formulating integrated-volatility for simulating risk-neutral probability density and calculating VaR
bull turning nonlinear dynamic auto-regression into static nonparametric regression
bull introducing adaptive statistical estimation methods to separate stationary and non-stationary factors
bull assessing modeling risk
bull paving a way to ldquostatistical financerdquo (market energy)
bull keeping the modeling framework flexible and adaptive under reflexivity
bull pricing profitable financial knowledges based on valuable dynamic kernels
Advantages on
Dynamic Domain
building robust amp adaptive models for financial engineering in magic domains
Dynamic Analysis of
Market Movements
various approaches from different perspectives and for different purposes
Categories of Analyzing Methodologies
Technical Analysis Stochastic-Process Modeling
Fundamental Analysis Inter-Market Analysis
Endogenous
ExogenousTraditional
Financial AnalysisAdvanced
Financial Engineering
Demand-Supply Mechanism
Growth-Value Perspective
Return-Risk Trade-off
Dynamics of Capital Flows
Part I
Elementary Ideas in
Technical Analysis
naiumlve financial signal processing
Reading Charts of
Market Movements
Technical Analysis ( 技術分析 ) = 看圖說故事
Correction ( 振盪整理 )
Uncertainty
Momentum
Finding Technical Patterns of
Market Demand-Supply
Momentum Risk Aversion and Bargain
Technical Analysis as
Financial Signal Processing
consistent Cycle-Leading Patterns out there
FilterEndogenousMarket Data Indicator
Market-CycleLeading PatternHistoric SimulationEmpirical
Strategy
fitting into noisesor
figuring out trendsor
creating cycles
bull Strength ndash Observation amp Explanation about Dynamic Phenomena
trying to explain filtered patterns based on
market demand-supply mechanism driven by market sentiment
eg
Moving Average (EMA MACD) Relative Strength Index Money Flow IndexBollinger Bands Support and Resistance Levels
bull Weakness ndash Formulation amp Correction about Dynamic Structure
lack of probabilistic formulation for
consistent strategy construction by risk-return trade-off and
systematic performance assessment
Strength and Weakness of
Technical Analysis
be aware of noisy illusions
Part II
Fundamental Structures in
Stochastic-Process Modeling
naiumlve capital market modeling
recognizing the random nature and formalizing the stochastic structure
Time Series of Periodic Return Rates
Mathematical Foundation of
Financial Engineering
Ri = (Si-Si-1)Si-1
Probabilistic Formulation L(Rii=1 hellip) ndash Joint Distribution
Dynamic Statistics Lθ(i) (Ri)i=1 hellip ndash Stochastic Evolution
Information Implication L(Si+1|Si)i=1 hellip ndash Prob Transition
Academic Canonical Frameworks of
Capital Market Modeling
Discrete-Time Version
(Auto-Regression)
Continuous-Time Version
(Stochastic Differential Equation)
IID Normal Sequence Geometric Brownian Motion
Ri = μ+σεi εi ~ N(01) dStSt = rmiddotdt + smiddotdWt
GARCH SVM (Mean-Reverting Process)
Ri = μ+σiεi εi ~ N(01)
σi 2 = α0+Σp
j=1αj εi-j2 +Σq
j=1βj σ i-j2
dStSt = rmiddotdt + |Vt|middotdWt
dVt = -kmiddot(Vt-c)middotdt + f(Vt)dZt
Generalization Generalization
Ri = μ(Ri-1 Ri-2 hellip)+σ (Ri-1 Ri-2 hellip) εi dStSt = Mtmiddotdt + VtmiddotdWt
could the models borrowed from physical systems well approach econ ones
Finding Clues for
Verifying Models
just simply a normal distributionor
a complicated mixture of normal distributions
tractable Dynamic Structure out there
dynamic tracingstatic de-mixing
bull Strength ndash Formulation amp Correction about Dynamic Structure
strong probabilistic formulation for
consistent strategy construction by risk-return trade-off and
systematic risk management (tools amp paradigms by financial engineering)
bull Weakness ndash Observation amp Explanation about Dynamic Phenomena
Ignoring (if any) ldquocyclic phenomenardquo and ldquoinvestment paradigmsrdquodue to
market demand-supply mechanism driven by
market sentiment and rationality
Strength and Weakness of
Stochastic-Process Modeling
be aware of simple biases
Part III
Reality amp
Lessons
itrsquos a jungle out there
bull Capital Markets are Complex Dynamic Systemsbull Non-linear Dynamic Mechanismbull Non-stationary Evolution due to changing Econ Conditions and Investment Paradigms
bull Multi-Component Framework of Market Behaviorbull Trend ndash Change Points Long-Term Evolutionary Structural Changesbull Seasonality ndash Periodic Factors bull Cycles ndash Dynamic Swings around Equilibriumbull Shocks ndash Unpredictable Impactsbull Noises ndash Endogenous and Environmental Uncertainties
bull Diversification in Market Constitutionbull Sentiment ndash Individual Investorsbull Rationality ndash Institutional Investors (Smart Money)bull Strategy ndash Arbitrageurs Risk Hedgers
bull Multi-Channel Infrastructure of Money Flowsbull Swifter and Swifter Trading Systemsbull Broader and Broader Asset Categoriesbull More Sophisticated and Complicated Financial Products and Trading Schemes
bull Reflexivity
The Complex Reality for
Thoughts
too many factors affecting market movements to figure out
can
deal with it
GARCH
Multi-Resolutionof
Complex Market Time Series
wavelet-based decomposition to figure out market behavior features
1974 Great Stock Market Capitulation
1987 Great Stock Market Crash
1989 Nikkei Bubble Burst
1997 Asian Currency Crisis
1998 LTCM Fallout
2000 Nasdaq (Tech) Bubble Burst
Hard Lessons from
Markets
dynamic risks beyond interpretation of stochastic volatility (no anomaly talk)
Part IV
Rational Memory Processes
a canonical methodological frameworkof
capital market modeling based on
financial signal processing
bull Theoretical Issues (about mathematical analysis)bull Dynamics ndash Demand Supply Mechanism
bull Randomness ndash Uncertainty Structure (multi-scale noise structure)
bull Practical Issues (about paradigms)bull Market Sentiment ndash Momentum Uncertainty
bull Market Rationality ndash Prediction Risk-Return Trade-Off
bull Market Strategy ndash Arbitrage Risk Hedging Schemes
bull Market Efficiency amp Completeness ndash Financial Infrastructures Products
bull Market Liquidity amp Friction ndash Trading Volumes Cost Turn-Over rate
bull Market Constitution ndash Economical Cultural Geopolitical Backgrounds
bull Technical Issues (about applications and implications)bull Model Identification ndash Parameter Estimation
bull Model Assessment ndash Modeling Risk (Modeling Bias Estimation Loss)
bull Model Adaptation ndash Coefficient Relations to Econ and Other Marketsrsquo Conditions
bull Model Extensibility ndash Extension to Absorb New Factors counting for ldquoAnomaliesrdquo
Prospects for
Modeling Capital Markets
setting a modeling methodological framework to incorporate the prospects
Challenges for
Modeling Capital Markets
bull Non-linearity amp Non-stationarity in Signal Dynamics
bull Complexity in Signal Structure
bull Noise Barrier (Overwhelming Noise-to-Signal Ratio)
bull Nonparametric Estimation (MLE does not make sense anymore here)
Curse of Dimensionality
1 2 3 4 5 6 7 8 9 10 11 12
Piecewise (Monthly) Constant Geometric Brownian Motion
Ri = μ(Ri-1 Ri-2 hellip)+σ (Ri-1 Ri-2 hellip) εi
Technical Foundationfor
Financial Signal Processing
Transformation Magic to break Curse of Dimensionality
Analyzing Signals over Fourier Frequency Domain
Analyzing Signals in Wavelet Multi-Resolution Framework
Complexity in Signal Structure
Non-linearity amp Non-stationarity in Signal Dynamics
Analyzing Signals over Dynamic Domain
in
Wavelet Multi-Resolution Framework
Fundamental Signal Processing Tasksfor
Financial Engineering
an objective way to format market patterns from experience
FilterHistoric
Time SeriesTechnicalIndicator
DiS0 S1 hellip Si
Di =Г(S0 hellip Si V0 hellip Vi |өi)
Dt =Гt(Sτ[0t])continuous-time approach
special interested format
Di =Г(R1 hellip Ri) Rj = (Sj-Sj-1)Sj-1
linear stationary case
Di = c1middotR1 + hellip + cimiddotRi Dt = int[0t]k(|τ-t|)middotSτ-1dSτ
Examples of
Dynamic Indicators
Dancing with Cycles
0 100 200 300 400 500 600 700-5
-4
-3
-2
-1
0
1
2
3
4
5
121951 022003
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
Dynamic Indicators Technical Indicators which serve to monitor and gauge market cycles
Critical Patternsof
Long-Term Cyclic Phenomena
0 50 100 150-2
-1
0
1
2
3
4
Jul 1993
Oct 1987
Nov 1981
Feb 1986
MaxUncertaintyLine
12-Month STTB Moving Average 12-Month SampP500 Return MA ()
Principle of Cyclic Hazard
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
1285 1290 0496
0401
Nikkei 225 SampP 500
TAIEX
Example Iof
Short-Horizon Dynamic Patterns
catching rebounding points and finding implicit trend forces
Fidelity Emerging Markets Fund (USD)
Fidelity Technology Fund (EUR) Fidelity American Growth Fund (USD)
Fidelity World Fund (EUR)
08182003 0120204 08182003 0120204
08182003 0120204 08182003 0120204
Index Value
20-Day STTB
Example IIof
Short-Horizon Dynamic Patterns
catching a rebounding and surging point
20-Day STTB
Example IIIof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Currency Triangular Arbitraging
12-Month MA of USD-vs-EUR Return Rate
12-Month MA of USD-vs-JPY Return Rate
12-Month MA of USD-vs-EUR 12-M STTB
12-Month MA of USD-vs-JPY 12-M STTB
Example IVof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Stock-Index Triangular Arbitraging
02132003 01162004
TWSEBKITWSE Cumulative Relative Return Rate (3)
TWSEELECTWSE Cumulative Relative Return Rate (3)
5-Day MA of TWSEBKITWSE Relative 20-Day STTB
5-Day MA of TWSEELECTWSE Relative 20-Day STTB
bull Physical Meanings - indicating practical market sense eg momentum uncertainty stability liquidity hellip etc
bull Cycle-Leading
bull Consistency amp Universality (Time amp Geography)
Conditionsof
Modeling Potential
warning markets might have no real intentions but filtersrsquo illusions
0 10 20 30 40 50 60-2
-1
0
1
2
3
4
011981 061985
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
- eg
Constructing Indicator-Oriented Strategieswith or without
Modeling
from empirical to theoretical
0 05 1 15 2 25 3 35 4-2
0
2
4
6
8
10H i+1
Si
Empirical Raw Optimal Strategy Theoretical Raw Optimal Strategy ΨΣ2
Methodological Framework of
Modeling Capital Markets
dynamics based on rationality oriented by memory filtered by dynamic kernel
Rational Memory Process
Ri+1-ri = Ψө(Di) + Ση(Di)middotεi+1
continuous-time approach (with a linear stationary filter)
dStSt = Ψө(int[0t]k(|τ-t|)middotSτ-1dSτ) middotdt + Ση(int[0t]k(|τ-t|)middotSτ
-1dSτ)middotdWt
Market Aggregation Rationality
Market Background Conditions
bull neatly constructing dynamic investment strategies on the dynamic domain
bull analytic calculation of risk-return trade-off curve via calculus of variation
bull easily formulating integrated-volatility for simulating risk-neutral probability density and calculating VaR
bull turning nonlinear dynamic auto-regression into static nonparametric regression
bull introducing adaptive statistical estimation methods to separate stationary and non-stationary factors
bull assessing modeling risk
bull paving a way to ldquostatistical financerdquo (market energy)
bull keeping the modeling framework flexible and adaptive under reflexivity
bull pricing profitable financial knowledges based on valuable dynamic kernels
Advantages on
Dynamic Domain
building robust amp adaptive models for financial engineering in magic domains
Part I
Elementary Ideas in
Technical Analysis
naiumlve financial signal processing
Reading Charts of
Market Movements
Technical Analysis ( 技術分析 ) = 看圖說故事
Correction ( 振盪整理 )
Uncertainty
Momentum
Finding Technical Patterns of
Market Demand-Supply
Momentum Risk Aversion and Bargain
Technical Analysis as
Financial Signal Processing
consistent Cycle-Leading Patterns out there
FilterEndogenousMarket Data Indicator
Market-CycleLeading PatternHistoric SimulationEmpirical
Strategy
fitting into noisesor
figuring out trendsor
creating cycles
bull Strength ndash Observation amp Explanation about Dynamic Phenomena
trying to explain filtered patterns based on
market demand-supply mechanism driven by market sentiment
eg
Moving Average (EMA MACD) Relative Strength Index Money Flow IndexBollinger Bands Support and Resistance Levels
bull Weakness ndash Formulation amp Correction about Dynamic Structure
lack of probabilistic formulation for
consistent strategy construction by risk-return trade-off and
systematic performance assessment
Strength and Weakness of
Technical Analysis
be aware of noisy illusions
Part II
Fundamental Structures in
Stochastic-Process Modeling
naiumlve capital market modeling
recognizing the random nature and formalizing the stochastic structure
Time Series of Periodic Return Rates
Mathematical Foundation of
Financial Engineering
Ri = (Si-Si-1)Si-1
Probabilistic Formulation L(Rii=1 hellip) ndash Joint Distribution
Dynamic Statistics Lθ(i) (Ri)i=1 hellip ndash Stochastic Evolution
Information Implication L(Si+1|Si)i=1 hellip ndash Prob Transition
Academic Canonical Frameworks of
Capital Market Modeling
Discrete-Time Version
(Auto-Regression)
Continuous-Time Version
(Stochastic Differential Equation)
IID Normal Sequence Geometric Brownian Motion
Ri = μ+σεi εi ~ N(01) dStSt = rmiddotdt + smiddotdWt
GARCH SVM (Mean-Reverting Process)
Ri = μ+σiεi εi ~ N(01)
σi 2 = α0+Σp
j=1αj εi-j2 +Σq
j=1βj σ i-j2
dStSt = rmiddotdt + |Vt|middotdWt
dVt = -kmiddot(Vt-c)middotdt + f(Vt)dZt
Generalization Generalization
Ri = μ(Ri-1 Ri-2 hellip)+σ (Ri-1 Ri-2 hellip) εi dStSt = Mtmiddotdt + VtmiddotdWt
could the models borrowed from physical systems well approach econ ones
Finding Clues for
Verifying Models
just simply a normal distributionor
a complicated mixture of normal distributions
tractable Dynamic Structure out there
dynamic tracingstatic de-mixing
bull Strength ndash Formulation amp Correction about Dynamic Structure
strong probabilistic formulation for
consistent strategy construction by risk-return trade-off and
systematic risk management (tools amp paradigms by financial engineering)
bull Weakness ndash Observation amp Explanation about Dynamic Phenomena
Ignoring (if any) ldquocyclic phenomenardquo and ldquoinvestment paradigmsrdquodue to
market demand-supply mechanism driven by
market sentiment and rationality
Strength and Weakness of
Stochastic-Process Modeling
be aware of simple biases
Part III
Reality amp
Lessons
itrsquos a jungle out there
bull Capital Markets are Complex Dynamic Systemsbull Non-linear Dynamic Mechanismbull Non-stationary Evolution due to changing Econ Conditions and Investment Paradigms
bull Multi-Component Framework of Market Behaviorbull Trend ndash Change Points Long-Term Evolutionary Structural Changesbull Seasonality ndash Periodic Factors bull Cycles ndash Dynamic Swings around Equilibriumbull Shocks ndash Unpredictable Impactsbull Noises ndash Endogenous and Environmental Uncertainties
bull Diversification in Market Constitutionbull Sentiment ndash Individual Investorsbull Rationality ndash Institutional Investors (Smart Money)bull Strategy ndash Arbitrageurs Risk Hedgers
bull Multi-Channel Infrastructure of Money Flowsbull Swifter and Swifter Trading Systemsbull Broader and Broader Asset Categoriesbull More Sophisticated and Complicated Financial Products and Trading Schemes
bull Reflexivity
The Complex Reality for
Thoughts
too many factors affecting market movements to figure out
can
deal with it
GARCH
Multi-Resolutionof
Complex Market Time Series
wavelet-based decomposition to figure out market behavior features
1974 Great Stock Market Capitulation
1987 Great Stock Market Crash
1989 Nikkei Bubble Burst
1997 Asian Currency Crisis
1998 LTCM Fallout
2000 Nasdaq (Tech) Bubble Burst
Hard Lessons from
Markets
dynamic risks beyond interpretation of stochastic volatility (no anomaly talk)
Part IV
Rational Memory Processes
a canonical methodological frameworkof
capital market modeling based on
financial signal processing
bull Theoretical Issues (about mathematical analysis)bull Dynamics ndash Demand Supply Mechanism
bull Randomness ndash Uncertainty Structure (multi-scale noise structure)
bull Practical Issues (about paradigms)bull Market Sentiment ndash Momentum Uncertainty
bull Market Rationality ndash Prediction Risk-Return Trade-Off
bull Market Strategy ndash Arbitrage Risk Hedging Schemes
bull Market Efficiency amp Completeness ndash Financial Infrastructures Products
bull Market Liquidity amp Friction ndash Trading Volumes Cost Turn-Over rate
bull Market Constitution ndash Economical Cultural Geopolitical Backgrounds
bull Technical Issues (about applications and implications)bull Model Identification ndash Parameter Estimation
bull Model Assessment ndash Modeling Risk (Modeling Bias Estimation Loss)
bull Model Adaptation ndash Coefficient Relations to Econ and Other Marketsrsquo Conditions
bull Model Extensibility ndash Extension to Absorb New Factors counting for ldquoAnomaliesrdquo
Prospects for
Modeling Capital Markets
setting a modeling methodological framework to incorporate the prospects
Challenges for
Modeling Capital Markets
bull Non-linearity amp Non-stationarity in Signal Dynamics
bull Complexity in Signal Structure
bull Noise Barrier (Overwhelming Noise-to-Signal Ratio)
bull Nonparametric Estimation (MLE does not make sense anymore here)
Curse of Dimensionality
1 2 3 4 5 6 7 8 9 10 11 12
Piecewise (Monthly) Constant Geometric Brownian Motion
Ri = μ(Ri-1 Ri-2 hellip)+σ (Ri-1 Ri-2 hellip) εi
Technical Foundationfor
Financial Signal Processing
Transformation Magic to break Curse of Dimensionality
Analyzing Signals over Fourier Frequency Domain
Analyzing Signals in Wavelet Multi-Resolution Framework
Complexity in Signal Structure
Non-linearity amp Non-stationarity in Signal Dynamics
Analyzing Signals over Dynamic Domain
in
Wavelet Multi-Resolution Framework
Fundamental Signal Processing Tasksfor
Financial Engineering
an objective way to format market patterns from experience
FilterHistoric
Time SeriesTechnicalIndicator
DiS0 S1 hellip Si
Di =Г(S0 hellip Si V0 hellip Vi |өi)
Dt =Гt(Sτ[0t])continuous-time approach
special interested format
Di =Г(R1 hellip Ri) Rj = (Sj-Sj-1)Sj-1
linear stationary case
Di = c1middotR1 + hellip + cimiddotRi Dt = int[0t]k(|τ-t|)middotSτ-1dSτ
Examples of
Dynamic Indicators
Dancing with Cycles
0 100 200 300 400 500 600 700-5
-4
-3
-2
-1
0
1
2
3
4
5
121951 022003
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
Dynamic Indicators Technical Indicators which serve to monitor and gauge market cycles
Critical Patternsof
Long-Term Cyclic Phenomena
0 50 100 150-2
-1
0
1
2
3
4
Jul 1993
Oct 1987
Nov 1981
Feb 1986
MaxUncertaintyLine
12-Month STTB Moving Average 12-Month SampP500 Return MA ()
Principle of Cyclic Hazard
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
1285 1290 0496
0401
Nikkei 225 SampP 500
TAIEX
Example Iof
Short-Horizon Dynamic Patterns
catching rebounding points and finding implicit trend forces
Fidelity Emerging Markets Fund (USD)
Fidelity Technology Fund (EUR) Fidelity American Growth Fund (USD)
Fidelity World Fund (EUR)
08182003 0120204 08182003 0120204
08182003 0120204 08182003 0120204
Index Value
20-Day STTB
Example IIof
Short-Horizon Dynamic Patterns
catching a rebounding and surging point
20-Day STTB
Example IIIof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Currency Triangular Arbitraging
12-Month MA of USD-vs-EUR Return Rate
12-Month MA of USD-vs-JPY Return Rate
12-Month MA of USD-vs-EUR 12-M STTB
12-Month MA of USD-vs-JPY 12-M STTB
Example IVof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Stock-Index Triangular Arbitraging
02132003 01162004
TWSEBKITWSE Cumulative Relative Return Rate (3)
TWSEELECTWSE Cumulative Relative Return Rate (3)
5-Day MA of TWSEBKITWSE Relative 20-Day STTB
5-Day MA of TWSEELECTWSE Relative 20-Day STTB
bull Physical Meanings - indicating practical market sense eg momentum uncertainty stability liquidity hellip etc
bull Cycle-Leading
bull Consistency amp Universality (Time amp Geography)
Conditionsof
Modeling Potential
warning markets might have no real intentions but filtersrsquo illusions
0 10 20 30 40 50 60-2
-1
0
1
2
3
4
011981 061985
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
- eg
Constructing Indicator-Oriented Strategieswith or without
Modeling
from empirical to theoretical
0 05 1 15 2 25 3 35 4-2
0
2
4
6
8
10H i+1
Si
Empirical Raw Optimal Strategy Theoretical Raw Optimal Strategy ΨΣ2
Methodological Framework of
Modeling Capital Markets
dynamics based on rationality oriented by memory filtered by dynamic kernel
Rational Memory Process
Ri+1-ri = Ψө(Di) + Ση(Di)middotεi+1
continuous-time approach (with a linear stationary filter)
dStSt = Ψө(int[0t]k(|τ-t|)middotSτ-1dSτ) middotdt + Ση(int[0t]k(|τ-t|)middotSτ
-1dSτ)middotdWt
Market Aggregation Rationality
Market Background Conditions
bull neatly constructing dynamic investment strategies on the dynamic domain
bull analytic calculation of risk-return trade-off curve via calculus of variation
bull easily formulating integrated-volatility for simulating risk-neutral probability density and calculating VaR
bull turning nonlinear dynamic auto-regression into static nonparametric regression
bull introducing adaptive statistical estimation methods to separate stationary and non-stationary factors
bull assessing modeling risk
bull paving a way to ldquostatistical financerdquo (market energy)
bull keeping the modeling framework flexible and adaptive under reflexivity
bull pricing profitable financial knowledges based on valuable dynamic kernels
Advantages on
Dynamic Domain
building robust amp adaptive models for financial engineering in magic domains
Reading Charts of
Market Movements
Technical Analysis ( 技術分析 ) = 看圖說故事
Correction ( 振盪整理 )
Uncertainty
Momentum
Finding Technical Patterns of
Market Demand-Supply
Momentum Risk Aversion and Bargain
Technical Analysis as
Financial Signal Processing
consistent Cycle-Leading Patterns out there
FilterEndogenousMarket Data Indicator
Market-CycleLeading PatternHistoric SimulationEmpirical
Strategy
fitting into noisesor
figuring out trendsor
creating cycles
bull Strength ndash Observation amp Explanation about Dynamic Phenomena
trying to explain filtered patterns based on
market demand-supply mechanism driven by market sentiment
eg
Moving Average (EMA MACD) Relative Strength Index Money Flow IndexBollinger Bands Support and Resistance Levels
bull Weakness ndash Formulation amp Correction about Dynamic Structure
lack of probabilistic formulation for
consistent strategy construction by risk-return trade-off and
systematic performance assessment
Strength and Weakness of
Technical Analysis
be aware of noisy illusions
Part II
Fundamental Structures in
Stochastic-Process Modeling
naiumlve capital market modeling
recognizing the random nature and formalizing the stochastic structure
Time Series of Periodic Return Rates
Mathematical Foundation of
Financial Engineering
Ri = (Si-Si-1)Si-1
Probabilistic Formulation L(Rii=1 hellip) ndash Joint Distribution
Dynamic Statistics Lθ(i) (Ri)i=1 hellip ndash Stochastic Evolution
Information Implication L(Si+1|Si)i=1 hellip ndash Prob Transition
Academic Canonical Frameworks of
Capital Market Modeling
Discrete-Time Version
(Auto-Regression)
Continuous-Time Version
(Stochastic Differential Equation)
IID Normal Sequence Geometric Brownian Motion
Ri = μ+σεi εi ~ N(01) dStSt = rmiddotdt + smiddotdWt
GARCH SVM (Mean-Reverting Process)
Ri = μ+σiεi εi ~ N(01)
σi 2 = α0+Σp
j=1αj εi-j2 +Σq
j=1βj σ i-j2
dStSt = rmiddotdt + |Vt|middotdWt
dVt = -kmiddot(Vt-c)middotdt + f(Vt)dZt
Generalization Generalization
Ri = μ(Ri-1 Ri-2 hellip)+σ (Ri-1 Ri-2 hellip) εi dStSt = Mtmiddotdt + VtmiddotdWt
could the models borrowed from physical systems well approach econ ones
Finding Clues for
Verifying Models
just simply a normal distributionor
a complicated mixture of normal distributions
tractable Dynamic Structure out there
dynamic tracingstatic de-mixing
bull Strength ndash Formulation amp Correction about Dynamic Structure
strong probabilistic formulation for
consistent strategy construction by risk-return trade-off and
systematic risk management (tools amp paradigms by financial engineering)
bull Weakness ndash Observation amp Explanation about Dynamic Phenomena
Ignoring (if any) ldquocyclic phenomenardquo and ldquoinvestment paradigmsrdquodue to
market demand-supply mechanism driven by
market sentiment and rationality
Strength and Weakness of
Stochastic-Process Modeling
be aware of simple biases
Part III
Reality amp
Lessons
itrsquos a jungle out there
bull Capital Markets are Complex Dynamic Systemsbull Non-linear Dynamic Mechanismbull Non-stationary Evolution due to changing Econ Conditions and Investment Paradigms
bull Multi-Component Framework of Market Behaviorbull Trend ndash Change Points Long-Term Evolutionary Structural Changesbull Seasonality ndash Periodic Factors bull Cycles ndash Dynamic Swings around Equilibriumbull Shocks ndash Unpredictable Impactsbull Noises ndash Endogenous and Environmental Uncertainties
bull Diversification in Market Constitutionbull Sentiment ndash Individual Investorsbull Rationality ndash Institutional Investors (Smart Money)bull Strategy ndash Arbitrageurs Risk Hedgers
bull Multi-Channel Infrastructure of Money Flowsbull Swifter and Swifter Trading Systemsbull Broader and Broader Asset Categoriesbull More Sophisticated and Complicated Financial Products and Trading Schemes
bull Reflexivity
The Complex Reality for
Thoughts
too many factors affecting market movements to figure out
can
deal with it
GARCH
Multi-Resolutionof
Complex Market Time Series
wavelet-based decomposition to figure out market behavior features
1974 Great Stock Market Capitulation
1987 Great Stock Market Crash
1989 Nikkei Bubble Burst
1997 Asian Currency Crisis
1998 LTCM Fallout
2000 Nasdaq (Tech) Bubble Burst
Hard Lessons from
Markets
dynamic risks beyond interpretation of stochastic volatility (no anomaly talk)
Part IV
Rational Memory Processes
a canonical methodological frameworkof
capital market modeling based on
financial signal processing
bull Theoretical Issues (about mathematical analysis)bull Dynamics ndash Demand Supply Mechanism
bull Randomness ndash Uncertainty Structure (multi-scale noise structure)
bull Practical Issues (about paradigms)bull Market Sentiment ndash Momentum Uncertainty
bull Market Rationality ndash Prediction Risk-Return Trade-Off
bull Market Strategy ndash Arbitrage Risk Hedging Schemes
bull Market Efficiency amp Completeness ndash Financial Infrastructures Products
bull Market Liquidity amp Friction ndash Trading Volumes Cost Turn-Over rate
bull Market Constitution ndash Economical Cultural Geopolitical Backgrounds
bull Technical Issues (about applications and implications)bull Model Identification ndash Parameter Estimation
bull Model Assessment ndash Modeling Risk (Modeling Bias Estimation Loss)
bull Model Adaptation ndash Coefficient Relations to Econ and Other Marketsrsquo Conditions
bull Model Extensibility ndash Extension to Absorb New Factors counting for ldquoAnomaliesrdquo
Prospects for
Modeling Capital Markets
setting a modeling methodological framework to incorporate the prospects
Challenges for
Modeling Capital Markets
bull Non-linearity amp Non-stationarity in Signal Dynamics
bull Complexity in Signal Structure
bull Noise Barrier (Overwhelming Noise-to-Signal Ratio)
bull Nonparametric Estimation (MLE does not make sense anymore here)
Curse of Dimensionality
1 2 3 4 5 6 7 8 9 10 11 12
Piecewise (Monthly) Constant Geometric Brownian Motion
Ri = μ(Ri-1 Ri-2 hellip)+σ (Ri-1 Ri-2 hellip) εi
Technical Foundationfor
Financial Signal Processing
Transformation Magic to break Curse of Dimensionality
Analyzing Signals over Fourier Frequency Domain
Analyzing Signals in Wavelet Multi-Resolution Framework
Complexity in Signal Structure
Non-linearity amp Non-stationarity in Signal Dynamics
Analyzing Signals over Dynamic Domain
in
Wavelet Multi-Resolution Framework
Fundamental Signal Processing Tasksfor
Financial Engineering
an objective way to format market patterns from experience
FilterHistoric
Time SeriesTechnicalIndicator
DiS0 S1 hellip Si
Di =Г(S0 hellip Si V0 hellip Vi |өi)
Dt =Гt(Sτ[0t])continuous-time approach
special interested format
Di =Г(R1 hellip Ri) Rj = (Sj-Sj-1)Sj-1
linear stationary case
Di = c1middotR1 + hellip + cimiddotRi Dt = int[0t]k(|τ-t|)middotSτ-1dSτ
Examples of
Dynamic Indicators
Dancing with Cycles
0 100 200 300 400 500 600 700-5
-4
-3
-2
-1
0
1
2
3
4
5
121951 022003
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
Dynamic Indicators Technical Indicators which serve to monitor and gauge market cycles
Critical Patternsof
Long-Term Cyclic Phenomena
0 50 100 150-2
-1
0
1
2
3
4
Jul 1993
Oct 1987
Nov 1981
Feb 1986
MaxUncertaintyLine
12-Month STTB Moving Average 12-Month SampP500 Return MA ()
Principle of Cyclic Hazard
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
1285 1290 0496
0401
Nikkei 225 SampP 500
TAIEX
Example Iof
Short-Horizon Dynamic Patterns
catching rebounding points and finding implicit trend forces
Fidelity Emerging Markets Fund (USD)
Fidelity Technology Fund (EUR) Fidelity American Growth Fund (USD)
Fidelity World Fund (EUR)
08182003 0120204 08182003 0120204
08182003 0120204 08182003 0120204
Index Value
20-Day STTB
Example IIof
Short-Horizon Dynamic Patterns
catching a rebounding and surging point
20-Day STTB
Example IIIof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Currency Triangular Arbitraging
12-Month MA of USD-vs-EUR Return Rate
12-Month MA of USD-vs-JPY Return Rate
12-Month MA of USD-vs-EUR 12-M STTB
12-Month MA of USD-vs-JPY 12-M STTB
Example IVof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Stock-Index Triangular Arbitraging
02132003 01162004
TWSEBKITWSE Cumulative Relative Return Rate (3)
TWSEELECTWSE Cumulative Relative Return Rate (3)
5-Day MA of TWSEBKITWSE Relative 20-Day STTB
5-Day MA of TWSEELECTWSE Relative 20-Day STTB
bull Physical Meanings - indicating practical market sense eg momentum uncertainty stability liquidity hellip etc
bull Cycle-Leading
bull Consistency amp Universality (Time amp Geography)
Conditionsof
Modeling Potential
warning markets might have no real intentions but filtersrsquo illusions
0 10 20 30 40 50 60-2
-1
0
1
2
3
4
011981 061985
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
- eg
Constructing Indicator-Oriented Strategieswith or without
Modeling
from empirical to theoretical
0 05 1 15 2 25 3 35 4-2
0
2
4
6
8
10H i+1
Si
Empirical Raw Optimal Strategy Theoretical Raw Optimal Strategy ΨΣ2
Methodological Framework of
Modeling Capital Markets
dynamics based on rationality oriented by memory filtered by dynamic kernel
Rational Memory Process
Ri+1-ri = Ψө(Di) + Ση(Di)middotεi+1
continuous-time approach (with a linear stationary filter)
dStSt = Ψө(int[0t]k(|τ-t|)middotSτ-1dSτ) middotdt + Ση(int[0t]k(|τ-t|)middotSτ
-1dSτ)middotdWt
Market Aggregation Rationality
Market Background Conditions
bull neatly constructing dynamic investment strategies on the dynamic domain
bull analytic calculation of risk-return trade-off curve via calculus of variation
bull easily formulating integrated-volatility for simulating risk-neutral probability density and calculating VaR
bull turning nonlinear dynamic auto-regression into static nonparametric regression
bull introducing adaptive statistical estimation methods to separate stationary and non-stationary factors
bull assessing modeling risk
bull paving a way to ldquostatistical financerdquo (market energy)
bull keeping the modeling framework flexible and adaptive under reflexivity
bull pricing profitable financial knowledges based on valuable dynamic kernels
Advantages on
Dynamic Domain
building robust amp adaptive models for financial engineering in magic domains
Finding Technical Patterns of
Market Demand-Supply
Momentum Risk Aversion and Bargain
Technical Analysis as
Financial Signal Processing
consistent Cycle-Leading Patterns out there
FilterEndogenousMarket Data Indicator
Market-CycleLeading PatternHistoric SimulationEmpirical
Strategy
fitting into noisesor
figuring out trendsor
creating cycles
bull Strength ndash Observation amp Explanation about Dynamic Phenomena
trying to explain filtered patterns based on
market demand-supply mechanism driven by market sentiment
eg
Moving Average (EMA MACD) Relative Strength Index Money Flow IndexBollinger Bands Support and Resistance Levels
bull Weakness ndash Formulation amp Correction about Dynamic Structure
lack of probabilistic formulation for
consistent strategy construction by risk-return trade-off and
systematic performance assessment
Strength and Weakness of
Technical Analysis
be aware of noisy illusions
Part II
Fundamental Structures in
Stochastic-Process Modeling
naiumlve capital market modeling
recognizing the random nature and formalizing the stochastic structure
Time Series of Periodic Return Rates
Mathematical Foundation of
Financial Engineering
Ri = (Si-Si-1)Si-1
Probabilistic Formulation L(Rii=1 hellip) ndash Joint Distribution
Dynamic Statistics Lθ(i) (Ri)i=1 hellip ndash Stochastic Evolution
Information Implication L(Si+1|Si)i=1 hellip ndash Prob Transition
Academic Canonical Frameworks of
Capital Market Modeling
Discrete-Time Version
(Auto-Regression)
Continuous-Time Version
(Stochastic Differential Equation)
IID Normal Sequence Geometric Brownian Motion
Ri = μ+σεi εi ~ N(01) dStSt = rmiddotdt + smiddotdWt
GARCH SVM (Mean-Reverting Process)
Ri = μ+σiεi εi ~ N(01)
σi 2 = α0+Σp
j=1αj εi-j2 +Σq
j=1βj σ i-j2
dStSt = rmiddotdt + |Vt|middotdWt
dVt = -kmiddot(Vt-c)middotdt + f(Vt)dZt
Generalization Generalization
Ri = μ(Ri-1 Ri-2 hellip)+σ (Ri-1 Ri-2 hellip) εi dStSt = Mtmiddotdt + VtmiddotdWt
could the models borrowed from physical systems well approach econ ones
Finding Clues for
Verifying Models
just simply a normal distributionor
a complicated mixture of normal distributions
tractable Dynamic Structure out there
dynamic tracingstatic de-mixing
bull Strength ndash Formulation amp Correction about Dynamic Structure
strong probabilistic formulation for
consistent strategy construction by risk-return trade-off and
systematic risk management (tools amp paradigms by financial engineering)
bull Weakness ndash Observation amp Explanation about Dynamic Phenomena
Ignoring (if any) ldquocyclic phenomenardquo and ldquoinvestment paradigmsrdquodue to
market demand-supply mechanism driven by
market sentiment and rationality
Strength and Weakness of
Stochastic-Process Modeling
be aware of simple biases
Part III
Reality amp
Lessons
itrsquos a jungle out there
bull Capital Markets are Complex Dynamic Systemsbull Non-linear Dynamic Mechanismbull Non-stationary Evolution due to changing Econ Conditions and Investment Paradigms
bull Multi-Component Framework of Market Behaviorbull Trend ndash Change Points Long-Term Evolutionary Structural Changesbull Seasonality ndash Periodic Factors bull Cycles ndash Dynamic Swings around Equilibriumbull Shocks ndash Unpredictable Impactsbull Noises ndash Endogenous and Environmental Uncertainties
bull Diversification in Market Constitutionbull Sentiment ndash Individual Investorsbull Rationality ndash Institutional Investors (Smart Money)bull Strategy ndash Arbitrageurs Risk Hedgers
bull Multi-Channel Infrastructure of Money Flowsbull Swifter and Swifter Trading Systemsbull Broader and Broader Asset Categoriesbull More Sophisticated and Complicated Financial Products and Trading Schemes
bull Reflexivity
The Complex Reality for
Thoughts
too many factors affecting market movements to figure out
can
deal with it
GARCH
Multi-Resolutionof
Complex Market Time Series
wavelet-based decomposition to figure out market behavior features
1974 Great Stock Market Capitulation
1987 Great Stock Market Crash
1989 Nikkei Bubble Burst
1997 Asian Currency Crisis
1998 LTCM Fallout
2000 Nasdaq (Tech) Bubble Burst
Hard Lessons from
Markets
dynamic risks beyond interpretation of stochastic volatility (no anomaly talk)
Part IV
Rational Memory Processes
a canonical methodological frameworkof
capital market modeling based on
financial signal processing
bull Theoretical Issues (about mathematical analysis)bull Dynamics ndash Demand Supply Mechanism
bull Randomness ndash Uncertainty Structure (multi-scale noise structure)
bull Practical Issues (about paradigms)bull Market Sentiment ndash Momentum Uncertainty
bull Market Rationality ndash Prediction Risk-Return Trade-Off
bull Market Strategy ndash Arbitrage Risk Hedging Schemes
bull Market Efficiency amp Completeness ndash Financial Infrastructures Products
bull Market Liquidity amp Friction ndash Trading Volumes Cost Turn-Over rate
bull Market Constitution ndash Economical Cultural Geopolitical Backgrounds
bull Technical Issues (about applications and implications)bull Model Identification ndash Parameter Estimation
bull Model Assessment ndash Modeling Risk (Modeling Bias Estimation Loss)
bull Model Adaptation ndash Coefficient Relations to Econ and Other Marketsrsquo Conditions
bull Model Extensibility ndash Extension to Absorb New Factors counting for ldquoAnomaliesrdquo
Prospects for
Modeling Capital Markets
setting a modeling methodological framework to incorporate the prospects
Challenges for
Modeling Capital Markets
bull Non-linearity amp Non-stationarity in Signal Dynamics
bull Complexity in Signal Structure
bull Noise Barrier (Overwhelming Noise-to-Signal Ratio)
bull Nonparametric Estimation (MLE does not make sense anymore here)
Curse of Dimensionality
1 2 3 4 5 6 7 8 9 10 11 12
Piecewise (Monthly) Constant Geometric Brownian Motion
Ri = μ(Ri-1 Ri-2 hellip)+σ (Ri-1 Ri-2 hellip) εi
Technical Foundationfor
Financial Signal Processing
Transformation Magic to break Curse of Dimensionality
Analyzing Signals over Fourier Frequency Domain
Analyzing Signals in Wavelet Multi-Resolution Framework
Complexity in Signal Structure
Non-linearity amp Non-stationarity in Signal Dynamics
Analyzing Signals over Dynamic Domain
in
Wavelet Multi-Resolution Framework
Fundamental Signal Processing Tasksfor
Financial Engineering
an objective way to format market patterns from experience
FilterHistoric
Time SeriesTechnicalIndicator
DiS0 S1 hellip Si
Di =Г(S0 hellip Si V0 hellip Vi |өi)
Dt =Гt(Sτ[0t])continuous-time approach
special interested format
Di =Г(R1 hellip Ri) Rj = (Sj-Sj-1)Sj-1
linear stationary case
Di = c1middotR1 + hellip + cimiddotRi Dt = int[0t]k(|τ-t|)middotSτ-1dSτ
Examples of
Dynamic Indicators
Dancing with Cycles
0 100 200 300 400 500 600 700-5
-4
-3
-2
-1
0
1
2
3
4
5
121951 022003
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
Dynamic Indicators Technical Indicators which serve to monitor and gauge market cycles
Critical Patternsof
Long-Term Cyclic Phenomena
0 50 100 150-2
-1
0
1
2
3
4
Jul 1993
Oct 1987
Nov 1981
Feb 1986
MaxUncertaintyLine
12-Month STTB Moving Average 12-Month SampP500 Return MA ()
Principle of Cyclic Hazard
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
1285 1290 0496
0401
Nikkei 225 SampP 500
TAIEX
Example Iof
Short-Horizon Dynamic Patterns
catching rebounding points and finding implicit trend forces
Fidelity Emerging Markets Fund (USD)
Fidelity Technology Fund (EUR) Fidelity American Growth Fund (USD)
Fidelity World Fund (EUR)
08182003 0120204 08182003 0120204
08182003 0120204 08182003 0120204
Index Value
20-Day STTB
Example IIof
Short-Horizon Dynamic Patterns
catching a rebounding and surging point
20-Day STTB
Example IIIof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Currency Triangular Arbitraging
12-Month MA of USD-vs-EUR Return Rate
12-Month MA of USD-vs-JPY Return Rate
12-Month MA of USD-vs-EUR 12-M STTB
12-Month MA of USD-vs-JPY 12-M STTB
Example IVof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Stock-Index Triangular Arbitraging
02132003 01162004
TWSEBKITWSE Cumulative Relative Return Rate (3)
TWSEELECTWSE Cumulative Relative Return Rate (3)
5-Day MA of TWSEBKITWSE Relative 20-Day STTB
5-Day MA of TWSEELECTWSE Relative 20-Day STTB
bull Physical Meanings - indicating practical market sense eg momentum uncertainty stability liquidity hellip etc
bull Cycle-Leading
bull Consistency amp Universality (Time amp Geography)
Conditionsof
Modeling Potential
warning markets might have no real intentions but filtersrsquo illusions
0 10 20 30 40 50 60-2
-1
0
1
2
3
4
011981 061985
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
- eg
Constructing Indicator-Oriented Strategieswith or without
Modeling
from empirical to theoretical
0 05 1 15 2 25 3 35 4-2
0
2
4
6
8
10H i+1
Si
Empirical Raw Optimal Strategy Theoretical Raw Optimal Strategy ΨΣ2
Methodological Framework of
Modeling Capital Markets
dynamics based on rationality oriented by memory filtered by dynamic kernel
Rational Memory Process
Ri+1-ri = Ψө(Di) + Ση(Di)middotεi+1
continuous-time approach (with a linear stationary filter)
dStSt = Ψө(int[0t]k(|τ-t|)middotSτ-1dSτ) middotdt + Ση(int[0t]k(|τ-t|)middotSτ
-1dSτ)middotdWt
Market Aggregation Rationality
Market Background Conditions
bull neatly constructing dynamic investment strategies on the dynamic domain
bull analytic calculation of risk-return trade-off curve via calculus of variation
bull easily formulating integrated-volatility for simulating risk-neutral probability density and calculating VaR
bull turning nonlinear dynamic auto-regression into static nonparametric regression
bull introducing adaptive statistical estimation methods to separate stationary and non-stationary factors
bull assessing modeling risk
bull paving a way to ldquostatistical financerdquo (market energy)
bull keeping the modeling framework flexible and adaptive under reflexivity
bull pricing profitable financial knowledges based on valuable dynamic kernels
Advantages on
Dynamic Domain
building robust amp adaptive models for financial engineering in magic domains
Technical Analysis as
Financial Signal Processing
consistent Cycle-Leading Patterns out there
FilterEndogenousMarket Data Indicator
Market-CycleLeading PatternHistoric SimulationEmpirical
Strategy
fitting into noisesor
figuring out trendsor
creating cycles
bull Strength ndash Observation amp Explanation about Dynamic Phenomena
trying to explain filtered patterns based on
market demand-supply mechanism driven by market sentiment
eg
Moving Average (EMA MACD) Relative Strength Index Money Flow IndexBollinger Bands Support and Resistance Levels
bull Weakness ndash Formulation amp Correction about Dynamic Structure
lack of probabilistic formulation for
consistent strategy construction by risk-return trade-off and
systematic performance assessment
Strength and Weakness of
Technical Analysis
be aware of noisy illusions
Part II
Fundamental Structures in
Stochastic-Process Modeling
naiumlve capital market modeling
recognizing the random nature and formalizing the stochastic structure
Time Series of Periodic Return Rates
Mathematical Foundation of
Financial Engineering
Ri = (Si-Si-1)Si-1
Probabilistic Formulation L(Rii=1 hellip) ndash Joint Distribution
Dynamic Statistics Lθ(i) (Ri)i=1 hellip ndash Stochastic Evolution
Information Implication L(Si+1|Si)i=1 hellip ndash Prob Transition
Academic Canonical Frameworks of
Capital Market Modeling
Discrete-Time Version
(Auto-Regression)
Continuous-Time Version
(Stochastic Differential Equation)
IID Normal Sequence Geometric Brownian Motion
Ri = μ+σεi εi ~ N(01) dStSt = rmiddotdt + smiddotdWt
GARCH SVM (Mean-Reverting Process)
Ri = μ+σiεi εi ~ N(01)
σi 2 = α0+Σp
j=1αj εi-j2 +Σq
j=1βj σ i-j2
dStSt = rmiddotdt + |Vt|middotdWt
dVt = -kmiddot(Vt-c)middotdt + f(Vt)dZt
Generalization Generalization
Ri = μ(Ri-1 Ri-2 hellip)+σ (Ri-1 Ri-2 hellip) εi dStSt = Mtmiddotdt + VtmiddotdWt
could the models borrowed from physical systems well approach econ ones
Finding Clues for
Verifying Models
just simply a normal distributionor
a complicated mixture of normal distributions
tractable Dynamic Structure out there
dynamic tracingstatic de-mixing
bull Strength ndash Formulation amp Correction about Dynamic Structure
strong probabilistic formulation for
consistent strategy construction by risk-return trade-off and
systematic risk management (tools amp paradigms by financial engineering)
bull Weakness ndash Observation amp Explanation about Dynamic Phenomena
Ignoring (if any) ldquocyclic phenomenardquo and ldquoinvestment paradigmsrdquodue to
market demand-supply mechanism driven by
market sentiment and rationality
Strength and Weakness of
Stochastic-Process Modeling
be aware of simple biases
Part III
Reality amp
Lessons
itrsquos a jungle out there
bull Capital Markets are Complex Dynamic Systemsbull Non-linear Dynamic Mechanismbull Non-stationary Evolution due to changing Econ Conditions and Investment Paradigms
bull Multi-Component Framework of Market Behaviorbull Trend ndash Change Points Long-Term Evolutionary Structural Changesbull Seasonality ndash Periodic Factors bull Cycles ndash Dynamic Swings around Equilibriumbull Shocks ndash Unpredictable Impactsbull Noises ndash Endogenous and Environmental Uncertainties
bull Diversification in Market Constitutionbull Sentiment ndash Individual Investorsbull Rationality ndash Institutional Investors (Smart Money)bull Strategy ndash Arbitrageurs Risk Hedgers
bull Multi-Channel Infrastructure of Money Flowsbull Swifter and Swifter Trading Systemsbull Broader and Broader Asset Categoriesbull More Sophisticated and Complicated Financial Products and Trading Schemes
bull Reflexivity
The Complex Reality for
Thoughts
too many factors affecting market movements to figure out
can
deal with it
GARCH
Multi-Resolutionof
Complex Market Time Series
wavelet-based decomposition to figure out market behavior features
1974 Great Stock Market Capitulation
1987 Great Stock Market Crash
1989 Nikkei Bubble Burst
1997 Asian Currency Crisis
1998 LTCM Fallout
2000 Nasdaq (Tech) Bubble Burst
Hard Lessons from
Markets
dynamic risks beyond interpretation of stochastic volatility (no anomaly talk)
Part IV
Rational Memory Processes
a canonical methodological frameworkof
capital market modeling based on
financial signal processing
bull Theoretical Issues (about mathematical analysis)bull Dynamics ndash Demand Supply Mechanism
bull Randomness ndash Uncertainty Structure (multi-scale noise structure)
bull Practical Issues (about paradigms)bull Market Sentiment ndash Momentum Uncertainty
bull Market Rationality ndash Prediction Risk-Return Trade-Off
bull Market Strategy ndash Arbitrage Risk Hedging Schemes
bull Market Efficiency amp Completeness ndash Financial Infrastructures Products
bull Market Liquidity amp Friction ndash Trading Volumes Cost Turn-Over rate
bull Market Constitution ndash Economical Cultural Geopolitical Backgrounds
bull Technical Issues (about applications and implications)bull Model Identification ndash Parameter Estimation
bull Model Assessment ndash Modeling Risk (Modeling Bias Estimation Loss)
bull Model Adaptation ndash Coefficient Relations to Econ and Other Marketsrsquo Conditions
bull Model Extensibility ndash Extension to Absorb New Factors counting for ldquoAnomaliesrdquo
Prospects for
Modeling Capital Markets
setting a modeling methodological framework to incorporate the prospects
Challenges for
Modeling Capital Markets
bull Non-linearity amp Non-stationarity in Signal Dynamics
bull Complexity in Signal Structure
bull Noise Barrier (Overwhelming Noise-to-Signal Ratio)
bull Nonparametric Estimation (MLE does not make sense anymore here)
Curse of Dimensionality
1 2 3 4 5 6 7 8 9 10 11 12
Piecewise (Monthly) Constant Geometric Brownian Motion
Ri = μ(Ri-1 Ri-2 hellip)+σ (Ri-1 Ri-2 hellip) εi
Technical Foundationfor
Financial Signal Processing
Transformation Magic to break Curse of Dimensionality
Analyzing Signals over Fourier Frequency Domain
Analyzing Signals in Wavelet Multi-Resolution Framework
Complexity in Signal Structure
Non-linearity amp Non-stationarity in Signal Dynamics
Analyzing Signals over Dynamic Domain
in
Wavelet Multi-Resolution Framework
Fundamental Signal Processing Tasksfor
Financial Engineering
an objective way to format market patterns from experience
FilterHistoric
Time SeriesTechnicalIndicator
DiS0 S1 hellip Si
Di =Г(S0 hellip Si V0 hellip Vi |өi)
Dt =Гt(Sτ[0t])continuous-time approach
special interested format
Di =Г(R1 hellip Ri) Rj = (Sj-Sj-1)Sj-1
linear stationary case
Di = c1middotR1 + hellip + cimiddotRi Dt = int[0t]k(|τ-t|)middotSτ-1dSτ
Examples of
Dynamic Indicators
Dancing with Cycles
0 100 200 300 400 500 600 700-5
-4
-3
-2
-1
0
1
2
3
4
5
121951 022003
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
Dynamic Indicators Technical Indicators which serve to monitor and gauge market cycles
Critical Patternsof
Long-Term Cyclic Phenomena
0 50 100 150-2
-1
0
1
2
3
4
Jul 1993
Oct 1987
Nov 1981
Feb 1986
MaxUncertaintyLine
12-Month STTB Moving Average 12-Month SampP500 Return MA ()
Principle of Cyclic Hazard
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
1285 1290 0496
0401
Nikkei 225 SampP 500
TAIEX
Example Iof
Short-Horizon Dynamic Patterns
catching rebounding points and finding implicit trend forces
Fidelity Emerging Markets Fund (USD)
Fidelity Technology Fund (EUR) Fidelity American Growth Fund (USD)
Fidelity World Fund (EUR)
08182003 0120204 08182003 0120204
08182003 0120204 08182003 0120204
Index Value
20-Day STTB
Example IIof
Short-Horizon Dynamic Patterns
catching a rebounding and surging point
20-Day STTB
Example IIIof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Currency Triangular Arbitraging
12-Month MA of USD-vs-EUR Return Rate
12-Month MA of USD-vs-JPY Return Rate
12-Month MA of USD-vs-EUR 12-M STTB
12-Month MA of USD-vs-JPY 12-M STTB
Example IVof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Stock-Index Triangular Arbitraging
02132003 01162004
TWSEBKITWSE Cumulative Relative Return Rate (3)
TWSEELECTWSE Cumulative Relative Return Rate (3)
5-Day MA of TWSEBKITWSE Relative 20-Day STTB
5-Day MA of TWSEELECTWSE Relative 20-Day STTB
bull Physical Meanings - indicating practical market sense eg momentum uncertainty stability liquidity hellip etc
bull Cycle-Leading
bull Consistency amp Universality (Time amp Geography)
Conditionsof
Modeling Potential
warning markets might have no real intentions but filtersrsquo illusions
0 10 20 30 40 50 60-2
-1
0
1
2
3
4
011981 061985
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
- eg
Constructing Indicator-Oriented Strategieswith or without
Modeling
from empirical to theoretical
0 05 1 15 2 25 3 35 4-2
0
2
4
6
8
10H i+1
Si
Empirical Raw Optimal Strategy Theoretical Raw Optimal Strategy ΨΣ2
Methodological Framework of
Modeling Capital Markets
dynamics based on rationality oriented by memory filtered by dynamic kernel
Rational Memory Process
Ri+1-ri = Ψө(Di) + Ση(Di)middotεi+1
continuous-time approach (with a linear stationary filter)
dStSt = Ψө(int[0t]k(|τ-t|)middotSτ-1dSτ) middotdt + Ση(int[0t]k(|τ-t|)middotSτ
-1dSτ)middotdWt
Market Aggregation Rationality
Market Background Conditions
bull neatly constructing dynamic investment strategies on the dynamic domain
bull analytic calculation of risk-return trade-off curve via calculus of variation
bull easily formulating integrated-volatility for simulating risk-neutral probability density and calculating VaR
bull turning nonlinear dynamic auto-regression into static nonparametric regression
bull introducing adaptive statistical estimation methods to separate stationary and non-stationary factors
bull assessing modeling risk
bull paving a way to ldquostatistical financerdquo (market energy)
bull keeping the modeling framework flexible and adaptive under reflexivity
bull pricing profitable financial knowledges based on valuable dynamic kernels
Advantages on
Dynamic Domain
building robust amp adaptive models for financial engineering in magic domains
bull Strength ndash Observation amp Explanation about Dynamic Phenomena
trying to explain filtered patterns based on
market demand-supply mechanism driven by market sentiment
eg
Moving Average (EMA MACD) Relative Strength Index Money Flow IndexBollinger Bands Support and Resistance Levels
bull Weakness ndash Formulation amp Correction about Dynamic Structure
lack of probabilistic formulation for
consistent strategy construction by risk-return trade-off and
systematic performance assessment
Strength and Weakness of
Technical Analysis
be aware of noisy illusions
Part II
Fundamental Structures in
Stochastic-Process Modeling
naiumlve capital market modeling
recognizing the random nature and formalizing the stochastic structure
Time Series of Periodic Return Rates
Mathematical Foundation of
Financial Engineering
Ri = (Si-Si-1)Si-1
Probabilistic Formulation L(Rii=1 hellip) ndash Joint Distribution
Dynamic Statistics Lθ(i) (Ri)i=1 hellip ndash Stochastic Evolution
Information Implication L(Si+1|Si)i=1 hellip ndash Prob Transition
Academic Canonical Frameworks of
Capital Market Modeling
Discrete-Time Version
(Auto-Regression)
Continuous-Time Version
(Stochastic Differential Equation)
IID Normal Sequence Geometric Brownian Motion
Ri = μ+σεi εi ~ N(01) dStSt = rmiddotdt + smiddotdWt
GARCH SVM (Mean-Reverting Process)
Ri = μ+σiεi εi ~ N(01)
σi 2 = α0+Σp
j=1αj εi-j2 +Σq
j=1βj σ i-j2
dStSt = rmiddotdt + |Vt|middotdWt
dVt = -kmiddot(Vt-c)middotdt + f(Vt)dZt
Generalization Generalization
Ri = μ(Ri-1 Ri-2 hellip)+σ (Ri-1 Ri-2 hellip) εi dStSt = Mtmiddotdt + VtmiddotdWt
could the models borrowed from physical systems well approach econ ones
Finding Clues for
Verifying Models
just simply a normal distributionor
a complicated mixture of normal distributions
tractable Dynamic Structure out there
dynamic tracingstatic de-mixing
bull Strength ndash Formulation amp Correction about Dynamic Structure
strong probabilistic formulation for
consistent strategy construction by risk-return trade-off and
systematic risk management (tools amp paradigms by financial engineering)
bull Weakness ndash Observation amp Explanation about Dynamic Phenomena
Ignoring (if any) ldquocyclic phenomenardquo and ldquoinvestment paradigmsrdquodue to
market demand-supply mechanism driven by
market sentiment and rationality
Strength and Weakness of
Stochastic-Process Modeling
be aware of simple biases
Part III
Reality amp
Lessons
itrsquos a jungle out there
bull Capital Markets are Complex Dynamic Systemsbull Non-linear Dynamic Mechanismbull Non-stationary Evolution due to changing Econ Conditions and Investment Paradigms
bull Multi-Component Framework of Market Behaviorbull Trend ndash Change Points Long-Term Evolutionary Structural Changesbull Seasonality ndash Periodic Factors bull Cycles ndash Dynamic Swings around Equilibriumbull Shocks ndash Unpredictable Impactsbull Noises ndash Endogenous and Environmental Uncertainties
bull Diversification in Market Constitutionbull Sentiment ndash Individual Investorsbull Rationality ndash Institutional Investors (Smart Money)bull Strategy ndash Arbitrageurs Risk Hedgers
bull Multi-Channel Infrastructure of Money Flowsbull Swifter and Swifter Trading Systemsbull Broader and Broader Asset Categoriesbull More Sophisticated and Complicated Financial Products and Trading Schemes
bull Reflexivity
The Complex Reality for
Thoughts
too many factors affecting market movements to figure out
can
deal with it
GARCH
Multi-Resolutionof
Complex Market Time Series
wavelet-based decomposition to figure out market behavior features
1974 Great Stock Market Capitulation
1987 Great Stock Market Crash
1989 Nikkei Bubble Burst
1997 Asian Currency Crisis
1998 LTCM Fallout
2000 Nasdaq (Tech) Bubble Burst
Hard Lessons from
Markets
dynamic risks beyond interpretation of stochastic volatility (no anomaly talk)
Part IV
Rational Memory Processes
a canonical methodological frameworkof
capital market modeling based on
financial signal processing
bull Theoretical Issues (about mathematical analysis)bull Dynamics ndash Demand Supply Mechanism
bull Randomness ndash Uncertainty Structure (multi-scale noise structure)
bull Practical Issues (about paradigms)bull Market Sentiment ndash Momentum Uncertainty
bull Market Rationality ndash Prediction Risk-Return Trade-Off
bull Market Strategy ndash Arbitrage Risk Hedging Schemes
bull Market Efficiency amp Completeness ndash Financial Infrastructures Products
bull Market Liquidity amp Friction ndash Trading Volumes Cost Turn-Over rate
bull Market Constitution ndash Economical Cultural Geopolitical Backgrounds
bull Technical Issues (about applications and implications)bull Model Identification ndash Parameter Estimation
bull Model Assessment ndash Modeling Risk (Modeling Bias Estimation Loss)
bull Model Adaptation ndash Coefficient Relations to Econ and Other Marketsrsquo Conditions
bull Model Extensibility ndash Extension to Absorb New Factors counting for ldquoAnomaliesrdquo
Prospects for
Modeling Capital Markets
setting a modeling methodological framework to incorporate the prospects
Challenges for
Modeling Capital Markets
bull Non-linearity amp Non-stationarity in Signal Dynamics
bull Complexity in Signal Structure
bull Noise Barrier (Overwhelming Noise-to-Signal Ratio)
bull Nonparametric Estimation (MLE does not make sense anymore here)
Curse of Dimensionality
1 2 3 4 5 6 7 8 9 10 11 12
Piecewise (Monthly) Constant Geometric Brownian Motion
Ri = μ(Ri-1 Ri-2 hellip)+σ (Ri-1 Ri-2 hellip) εi
Technical Foundationfor
Financial Signal Processing
Transformation Magic to break Curse of Dimensionality
Analyzing Signals over Fourier Frequency Domain
Analyzing Signals in Wavelet Multi-Resolution Framework
Complexity in Signal Structure
Non-linearity amp Non-stationarity in Signal Dynamics
Analyzing Signals over Dynamic Domain
in
Wavelet Multi-Resolution Framework
Fundamental Signal Processing Tasksfor
Financial Engineering
an objective way to format market patterns from experience
FilterHistoric
Time SeriesTechnicalIndicator
DiS0 S1 hellip Si
Di =Г(S0 hellip Si V0 hellip Vi |өi)
Dt =Гt(Sτ[0t])continuous-time approach
special interested format
Di =Г(R1 hellip Ri) Rj = (Sj-Sj-1)Sj-1
linear stationary case
Di = c1middotR1 + hellip + cimiddotRi Dt = int[0t]k(|τ-t|)middotSτ-1dSτ
Examples of
Dynamic Indicators
Dancing with Cycles
0 100 200 300 400 500 600 700-5
-4
-3
-2
-1
0
1
2
3
4
5
121951 022003
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
Dynamic Indicators Technical Indicators which serve to monitor and gauge market cycles
Critical Patternsof
Long-Term Cyclic Phenomena
0 50 100 150-2
-1
0
1
2
3
4
Jul 1993
Oct 1987
Nov 1981
Feb 1986
MaxUncertaintyLine
12-Month STTB Moving Average 12-Month SampP500 Return MA ()
Principle of Cyclic Hazard
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
1285 1290 0496
0401
Nikkei 225 SampP 500
TAIEX
Example Iof
Short-Horizon Dynamic Patterns
catching rebounding points and finding implicit trend forces
Fidelity Emerging Markets Fund (USD)
Fidelity Technology Fund (EUR) Fidelity American Growth Fund (USD)
Fidelity World Fund (EUR)
08182003 0120204 08182003 0120204
08182003 0120204 08182003 0120204
Index Value
20-Day STTB
Example IIof
Short-Horizon Dynamic Patterns
catching a rebounding and surging point
20-Day STTB
Example IIIof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Currency Triangular Arbitraging
12-Month MA of USD-vs-EUR Return Rate
12-Month MA of USD-vs-JPY Return Rate
12-Month MA of USD-vs-EUR 12-M STTB
12-Month MA of USD-vs-JPY 12-M STTB
Example IVof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Stock-Index Triangular Arbitraging
02132003 01162004
TWSEBKITWSE Cumulative Relative Return Rate (3)
TWSEELECTWSE Cumulative Relative Return Rate (3)
5-Day MA of TWSEBKITWSE Relative 20-Day STTB
5-Day MA of TWSEELECTWSE Relative 20-Day STTB
bull Physical Meanings - indicating practical market sense eg momentum uncertainty stability liquidity hellip etc
bull Cycle-Leading
bull Consistency amp Universality (Time amp Geography)
Conditionsof
Modeling Potential
warning markets might have no real intentions but filtersrsquo illusions
0 10 20 30 40 50 60-2
-1
0
1
2
3
4
011981 061985
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
- eg
Constructing Indicator-Oriented Strategieswith or without
Modeling
from empirical to theoretical
0 05 1 15 2 25 3 35 4-2
0
2
4
6
8
10H i+1
Si
Empirical Raw Optimal Strategy Theoretical Raw Optimal Strategy ΨΣ2
Methodological Framework of
Modeling Capital Markets
dynamics based on rationality oriented by memory filtered by dynamic kernel
Rational Memory Process
Ri+1-ri = Ψө(Di) + Ση(Di)middotεi+1
continuous-time approach (with a linear stationary filter)
dStSt = Ψө(int[0t]k(|τ-t|)middotSτ-1dSτ) middotdt + Ση(int[0t]k(|τ-t|)middotSτ
-1dSτ)middotdWt
Market Aggregation Rationality
Market Background Conditions
bull neatly constructing dynamic investment strategies on the dynamic domain
bull analytic calculation of risk-return trade-off curve via calculus of variation
bull easily formulating integrated-volatility for simulating risk-neutral probability density and calculating VaR
bull turning nonlinear dynamic auto-regression into static nonparametric regression
bull introducing adaptive statistical estimation methods to separate stationary and non-stationary factors
bull assessing modeling risk
bull paving a way to ldquostatistical financerdquo (market energy)
bull keeping the modeling framework flexible and adaptive under reflexivity
bull pricing profitable financial knowledges based on valuable dynamic kernels
Advantages on
Dynamic Domain
building robust amp adaptive models for financial engineering in magic domains
Part II
Fundamental Structures in
Stochastic-Process Modeling
naiumlve capital market modeling
recognizing the random nature and formalizing the stochastic structure
Time Series of Periodic Return Rates
Mathematical Foundation of
Financial Engineering
Ri = (Si-Si-1)Si-1
Probabilistic Formulation L(Rii=1 hellip) ndash Joint Distribution
Dynamic Statistics Lθ(i) (Ri)i=1 hellip ndash Stochastic Evolution
Information Implication L(Si+1|Si)i=1 hellip ndash Prob Transition
Academic Canonical Frameworks of
Capital Market Modeling
Discrete-Time Version
(Auto-Regression)
Continuous-Time Version
(Stochastic Differential Equation)
IID Normal Sequence Geometric Brownian Motion
Ri = μ+σεi εi ~ N(01) dStSt = rmiddotdt + smiddotdWt
GARCH SVM (Mean-Reverting Process)
Ri = μ+σiεi εi ~ N(01)
σi 2 = α0+Σp
j=1αj εi-j2 +Σq
j=1βj σ i-j2
dStSt = rmiddotdt + |Vt|middotdWt
dVt = -kmiddot(Vt-c)middotdt + f(Vt)dZt
Generalization Generalization
Ri = μ(Ri-1 Ri-2 hellip)+σ (Ri-1 Ri-2 hellip) εi dStSt = Mtmiddotdt + VtmiddotdWt
could the models borrowed from physical systems well approach econ ones
Finding Clues for
Verifying Models
just simply a normal distributionor
a complicated mixture of normal distributions
tractable Dynamic Structure out there
dynamic tracingstatic de-mixing
bull Strength ndash Formulation amp Correction about Dynamic Structure
strong probabilistic formulation for
consistent strategy construction by risk-return trade-off and
systematic risk management (tools amp paradigms by financial engineering)
bull Weakness ndash Observation amp Explanation about Dynamic Phenomena
Ignoring (if any) ldquocyclic phenomenardquo and ldquoinvestment paradigmsrdquodue to
market demand-supply mechanism driven by
market sentiment and rationality
Strength and Weakness of
Stochastic-Process Modeling
be aware of simple biases
Part III
Reality amp
Lessons
itrsquos a jungle out there
bull Capital Markets are Complex Dynamic Systemsbull Non-linear Dynamic Mechanismbull Non-stationary Evolution due to changing Econ Conditions and Investment Paradigms
bull Multi-Component Framework of Market Behaviorbull Trend ndash Change Points Long-Term Evolutionary Structural Changesbull Seasonality ndash Periodic Factors bull Cycles ndash Dynamic Swings around Equilibriumbull Shocks ndash Unpredictable Impactsbull Noises ndash Endogenous and Environmental Uncertainties
bull Diversification in Market Constitutionbull Sentiment ndash Individual Investorsbull Rationality ndash Institutional Investors (Smart Money)bull Strategy ndash Arbitrageurs Risk Hedgers
bull Multi-Channel Infrastructure of Money Flowsbull Swifter and Swifter Trading Systemsbull Broader and Broader Asset Categoriesbull More Sophisticated and Complicated Financial Products and Trading Schemes
bull Reflexivity
The Complex Reality for
Thoughts
too many factors affecting market movements to figure out
can
deal with it
GARCH
Multi-Resolutionof
Complex Market Time Series
wavelet-based decomposition to figure out market behavior features
1974 Great Stock Market Capitulation
1987 Great Stock Market Crash
1989 Nikkei Bubble Burst
1997 Asian Currency Crisis
1998 LTCM Fallout
2000 Nasdaq (Tech) Bubble Burst
Hard Lessons from
Markets
dynamic risks beyond interpretation of stochastic volatility (no anomaly talk)
Part IV
Rational Memory Processes
a canonical methodological frameworkof
capital market modeling based on
financial signal processing
bull Theoretical Issues (about mathematical analysis)bull Dynamics ndash Demand Supply Mechanism
bull Randomness ndash Uncertainty Structure (multi-scale noise structure)
bull Practical Issues (about paradigms)bull Market Sentiment ndash Momentum Uncertainty
bull Market Rationality ndash Prediction Risk-Return Trade-Off
bull Market Strategy ndash Arbitrage Risk Hedging Schemes
bull Market Efficiency amp Completeness ndash Financial Infrastructures Products
bull Market Liquidity amp Friction ndash Trading Volumes Cost Turn-Over rate
bull Market Constitution ndash Economical Cultural Geopolitical Backgrounds
bull Technical Issues (about applications and implications)bull Model Identification ndash Parameter Estimation
bull Model Assessment ndash Modeling Risk (Modeling Bias Estimation Loss)
bull Model Adaptation ndash Coefficient Relations to Econ and Other Marketsrsquo Conditions
bull Model Extensibility ndash Extension to Absorb New Factors counting for ldquoAnomaliesrdquo
Prospects for
Modeling Capital Markets
setting a modeling methodological framework to incorporate the prospects
Challenges for
Modeling Capital Markets
bull Non-linearity amp Non-stationarity in Signal Dynamics
bull Complexity in Signal Structure
bull Noise Barrier (Overwhelming Noise-to-Signal Ratio)
bull Nonparametric Estimation (MLE does not make sense anymore here)
Curse of Dimensionality
1 2 3 4 5 6 7 8 9 10 11 12
Piecewise (Monthly) Constant Geometric Brownian Motion
Ri = μ(Ri-1 Ri-2 hellip)+σ (Ri-1 Ri-2 hellip) εi
Technical Foundationfor
Financial Signal Processing
Transformation Magic to break Curse of Dimensionality
Analyzing Signals over Fourier Frequency Domain
Analyzing Signals in Wavelet Multi-Resolution Framework
Complexity in Signal Structure
Non-linearity amp Non-stationarity in Signal Dynamics
Analyzing Signals over Dynamic Domain
in
Wavelet Multi-Resolution Framework
Fundamental Signal Processing Tasksfor
Financial Engineering
an objective way to format market patterns from experience
FilterHistoric
Time SeriesTechnicalIndicator
DiS0 S1 hellip Si
Di =Г(S0 hellip Si V0 hellip Vi |өi)
Dt =Гt(Sτ[0t])continuous-time approach
special interested format
Di =Г(R1 hellip Ri) Rj = (Sj-Sj-1)Sj-1
linear stationary case
Di = c1middotR1 + hellip + cimiddotRi Dt = int[0t]k(|τ-t|)middotSτ-1dSτ
Examples of
Dynamic Indicators
Dancing with Cycles
0 100 200 300 400 500 600 700-5
-4
-3
-2
-1
0
1
2
3
4
5
121951 022003
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
Dynamic Indicators Technical Indicators which serve to monitor and gauge market cycles
Critical Patternsof
Long-Term Cyclic Phenomena
0 50 100 150-2
-1
0
1
2
3
4
Jul 1993
Oct 1987
Nov 1981
Feb 1986
MaxUncertaintyLine
12-Month STTB Moving Average 12-Month SampP500 Return MA ()
Principle of Cyclic Hazard
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
1285 1290 0496
0401
Nikkei 225 SampP 500
TAIEX
Example Iof
Short-Horizon Dynamic Patterns
catching rebounding points and finding implicit trend forces
Fidelity Emerging Markets Fund (USD)
Fidelity Technology Fund (EUR) Fidelity American Growth Fund (USD)
Fidelity World Fund (EUR)
08182003 0120204 08182003 0120204
08182003 0120204 08182003 0120204
Index Value
20-Day STTB
Example IIof
Short-Horizon Dynamic Patterns
catching a rebounding and surging point
20-Day STTB
Example IIIof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Currency Triangular Arbitraging
12-Month MA of USD-vs-EUR Return Rate
12-Month MA of USD-vs-JPY Return Rate
12-Month MA of USD-vs-EUR 12-M STTB
12-Month MA of USD-vs-JPY 12-M STTB
Example IVof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Stock-Index Triangular Arbitraging
02132003 01162004
TWSEBKITWSE Cumulative Relative Return Rate (3)
TWSEELECTWSE Cumulative Relative Return Rate (3)
5-Day MA of TWSEBKITWSE Relative 20-Day STTB
5-Day MA of TWSEELECTWSE Relative 20-Day STTB
bull Physical Meanings - indicating practical market sense eg momentum uncertainty stability liquidity hellip etc
bull Cycle-Leading
bull Consistency amp Universality (Time amp Geography)
Conditionsof
Modeling Potential
warning markets might have no real intentions but filtersrsquo illusions
0 10 20 30 40 50 60-2
-1
0
1
2
3
4
011981 061985
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
- eg
Constructing Indicator-Oriented Strategieswith or without
Modeling
from empirical to theoretical
0 05 1 15 2 25 3 35 4-2
0
2
4
6
8
10H i+1
Si
Empirical Raw Optimal Strategy Theoretical Raw Optimal Strategy ΨΣ2
Methodological Framework of
Modeling Capital Markets
dynamics based on rationality oriented by memory filtered by dynamic kernel
Rational Memory Process
Ri+1-ri = Ψө(Di) + Ση(Di)middotεi+1
continuous-time approach (with a linear stationary filter)
dStSt = Ψө(int[0t]k(|τ-t|)middotSτ-1dSτ) middotdt + Ση(int[0t]k(|τ-t|)middotSτ
-1dSτ)middotdWt
Market Aggregation Rationality
Market Background Conditions
bull neatly constructing dynamic investment strategies on the dynamic domain
bull analytic calculation of risk-return trade-off curve via calculus of variation
bull easily formulating integrated-volatility for simulating risk-neutral probability density and calculating VaR
bull turning nonlinear dynamic auto-regression into static nonparametric regression
bull introducing adaptive statistical estimation methods to separate stationary and non-stationary factors
bull assessing modeling risk
bull paving a way to ldquostatistical financerdquo (market energy)
bull keeping the modeling framework flexible and adaptive under reflexivity
bull pricing profitable financial knowledges based on valuable dynamic kernels
Advantages on
Dynamic Domain
building robust amp adaptive models for financial engineering in magic domains
recognizing the random nature and formalizing the stochastic structure
Time Series of Periodic Return Rates
Mathematical Foundation of
Financial Engineering
Ri = (Si-Si-1)Si-1
Probabilistic Formulation L(Rii=1 hellip) ndash Joint Distribution
Dynamic Statistics Lθ(i) (Ri)i=1 hellip ndash Stochastic Evolution
Information Implication L(Si+1|Si)i=1 hellip ndash Prob Transition
Academic Canonical Frameworks of
Capital Market Modeling
Discrete-Time Version
(Auto-Regression)
Continuous-Time Version
(Stochastic Differential Equation)
IID Normal Sequence Geometric Brownian Motion
Ri = μ+σεi εi ~ N(01) dStSt = rmiddotdt + smiddotdWt
GARCH SVM (Mean-Reverting Process)
Ri = μ+σiεi εi ~ N(01)
σi 2 = α0+Σp
j=1αj εi-j2 +Σq
j=1βj σ i-j2
dStSt = rmiddotdt + |Vt|middotdWt
dVt = -kmiddot(Vt-c)middotdt + f(Vt)dZt
Generalization Generalization
Ri = μ(Ri-1 Ri-2 hellip)+σ (Ri-1 Ri-2 hellip) εi dStSt = Mtmiddotdt + VtmiddotdWt
could the models borrowed from physical systems well approach econ ones
Finding Clues for
Verifying Models
just simply a normal distributionor
a complicated mixture of normal distributions
tractable Dynamic Structure out there
dynamic tracingstatic de-mixing
bull Strength ndash Formulation amp Correction about Dynamic Structure
strong probabilistic formulation for
consistent strategy construction by risk-return trade-off and
systematic risk management (tools amp paradigms by financial engineering)
bull Weakness ndash Observation amp Explanation about Dynamic Phenomena
Ignoring (if any) ldquocyclic phenomenardquo and ldquoinvestment paradigmsrdquodue to
market demand-supply mechanism driven by
market sentiment and rationality
Strength and Weakness of
Stochastic-Process Modeling
be aware of simple biases
Part III
Reality amp
Lessons
itrsquos a jungle out there
bull Capital Markets are Complex Dynamic Systemsbull Non-linear Dynamic Mechanismbull Non-stationary Evolution due to changing Econ Conditions and Investment Paradigms
bull Multi-Component Framework of Market Behaviorbull Trend ndash Change Points Long-Term Evolutionary Structural Changesbull Seasonality ndash Periodic Factors bull Cycles ndash Dynamic Swings around Equilibriumbull Shocks ndash Unpredictable Impactsbull Noises ndash Endogenous and Environmental Uncertainties
bull Diversification in Market Constitutionbull Sentiment ndash Individual Investorsbull Rationality ndash Institutional Investors (Smart Money)bull Strategy ndash Arbitrageurs Risk Hedgers
bull Multi-Channel Infrastructure of Money Flowsbull Swifter and Swifter Trading Systemsbull Broader and Broader Asset Categoriesbull More Sophisticated and Complicated Financial Products and Trading Schemes
bull Reflexivity
The Complex Reality for
Thoughts
too many factors affecting market movements to figure out
can
deal with it
GARCH
Multi-Resolutionof
Complex Market Time Series
wavelet-based decomposition to figure out market behavior features
1974 Great Stock Market Capitulation
1987 Great Stock Market Crash
1989 Nikkei Bubble Burst
1997 Asian Currency Crisis
1998 LTCM Fallout
2000 Nasdaq (Tech) Bubble Burst
Hard Lessons from
Markets
dynamic risks beyond interpretation of stochastic volatility (no anomaly talk)
Part IV
Rational Memory Processes
a canonical methodological frameworkof
capital market modeling based on
financial signal processing
bull Theoretical Issues (about mathematical analysis)bull Dynamics ndash Demand Supply Mechanism
bull Randomness ndash Uncertainty Structure (multi-scale noise structure)
bull Practical Issues (about paradigms)bull Market Sentiment ndash Momentum Uncertainty
bull Market Rationality ndash Prediction Risk-Return Trade-Off
bull Market Strategy ndash Arbitrage Risk Hedging Schemes
bull Market Efficiency amp Completeness ndash Financial Infrastructures Products
bull Market Liquidity amp Friction ndash Trading Volumes Cost Turn-Over rate
bull Market Constitution ndash Economical Cultural Geopolitical Backgrounds
bull Technical Issues (about applications and implications)bull Model Identification ndash Parameter Estimation
bull Model Assessment ndash Modeling Risk (Modeling Bias Estimation Loss)
bull Model Adaptation ndash Coefficient Relations to Econ and Other Marketsrsquo Conditions
bull Model Extensibility ndash Extension to Absorb New Factors counting for ldquoAnomaliesrdquo
Prospects for
Modeling Capital Markets
setting a modeling methodological framework to incorporate the prospects
Challenges for
Modeling Capital Markets
bull Non-linearity amp Non-stationarity in Signal Dynamics
bull Complexity in Signal Structure
bull Noise Barrier (Overwhelming Noise-to-Signal Ratio)
bull Nonparametric Estimation (MLE does not make sense anymore here)
Curse of Dimensionality
1 2 3 4 5 6 7 8 9 10 11 12
Piecewise (Monthly) Constant Geometric Brownian Motion
Ri = μ(Ri-1 Ri-2 hellip)+σ (Ri-1 Ri-2 hellip) εi
Technical Foundationfor
Financial Signal Processing
Transformation Magic to break Curse of Dimensionality
Analyzing Signals over Fourier Frequency Domain
Analyzing Signals in Wavelet Multi-Resolution Framework
Complexity in Signal Structure
Non-linearity amp Non-stationarity in Signal Dynamics
Analyzing Signals over Dynamic Domain
in
Wavelet Multi-Resolution Framework
Fundamental Signal Processing Tasksfor
Financial Engineering
an objective way to format market patterns from experience
FilterHistoric
Time SeriesTechnicalIndicator
DiS0 S1 hellip Si
Di =Г(S0 hellip Si V0 hellip Vi |өi)
Dt =Гt(Sτ[0t])continuous-time approach
special interested format
Di =Г(R1 hellip Ri) Rj = (Sj-Sj-1)Sj-1
linear stationary case
Di = c1middotR1 + hellip + cimiddotRi Dt = int[0t]k(|τ-t|)middotSτ-1dSτ
Examples of
Dynamic Indicators
Dancing with Cycles
0 100 200 300 400 500 600 700-5
-4
-3
-2
-1
0
1
2
3
4
5
121951 022003
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
Dynamic Indicators Technical Indicators which serve to monitor and gauge market cycles
Critical Patternsof
Long-Term Cyclic Phenomena
0 50 100 150-2
-1
0
1
2
3
4
Jul 1993
Oct 1987
Nov 1981
Feb 1986
MaxUncertaintyLine
12-Month STTB Moving Average 12-Month SampP500 Return MA ()
Principle of Cyclic Hazard
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
1285 1290 0496
0401
Nikkei 225 SampP 500
TAIEX
Example Iof
Short-Horizon Dynamic Patterns
catching rebounding points and finding implicit trend forces
Fidelity Emerging Markets Fund (USD)
Fidelity Technology Fund (EUR) Fidelity American Growth Fund (USD)
Fidelity World Fund (EUR)
08182003 0120204 08182003 0120204
08182003 0120204 08182003 0120204
Index Value
20-Day STTB
Example IIof
Short-Horizon Dynamic Patterns
catching a rebounding and surging point
20-Day STTB
Example IIIof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Currency Triangular Arbitraging
12-Month MA of USD-vs-EUR Return Rate
12-Month MA of USD-vs-JPY Return Rate
12-Month MA of USD-vs-EUR 12-M STTB
12-Month MA of USD-vs-JPY 12-M STTB
Example IVof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Stock-Index Triangular Arbitraging
02132003 01162004
TWSEBKITWSE Cumulative Relative Return Rate (3)
TWSEELECTWSE Cumulative Relative Return Rate (3)
5-Day MA of TWSEBKITWSE Relative 20-Day STTB
5-Day MA of TWSEELECTWSE Relative 20-Day STTB
bull Physical Meanings - indicating practical market sense eg momentum uncertainty stability liquidity hellip etc
bull Cycle-Leading
bull Consistency amp Universality (Time amp Geography)
Conditionsof
Modeling Potential
warning markets might have no real intentions but filtersrsquo illusions
0 10 20 30 40 50 60-2
-1
0
1
2
3
4
011981 061985
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
- eg
Constructing Indicator-Oriented Strategieswith or without
Modeling
from empirical to theoretical
0 05 1 15 2 25 3 35 4-2
0
2
4
6
8
10H i+1
Si
Empirical Raw Optimal Strategy Theoretical Raw Optimal Strategy ΨΣ2
Methodological Framework of
Modeling Capital Markets
dynamics based on rationality oriented by memory filtered by dynamic kernel
Rational Memory Process
Ri+1-ri = Ψө(Di) + Ση(Di)middotεi+1
continuous-time approach (with a linear stationary filter)
dStSt = Ψө(int[0t]k(|τ-t|)middotSτ-1dSτ) middotdt + Ση(int[0t]k(|τ-t|)middotSτ
-1dSτ)middotdWt
Market Aggregation Rationality
Market Background Conditions
bull neatly constructing dynamic investment strategies on the dynamic domain
bull analytic calculation of risk-return trade-off curve via calculus of variation
bull easily formulating integrated-volatility for simulating risk-neutral probability density and calculating VaR
bull turning nonlinear dynamic auto-regression into static nonparametric regression
bull introducing adaptive statistical estimation methods to separate stationary and non-stationary factors
bull assessing modeling risk
bull paving a way to ldquostatistical financerdquo (market energy)
bull keeping the modeling framework flexible and adaptive under reflexivity
bull pricing profitable financial knowledges based on valuable dynamic kernels
Advantages on
Dynamic Domain
building robust amp adaptive models for financial engineering in magic domains
Academic Canonical Frameworks of
Capital Market Modeling
Discrete-Time Version
(Auto-Regression)
Continuous-Time Version
(Stochastic Differential Equation)
IID Normal Sequence Geometric Brownian Motion
Ri = μ+σεi εi ~ N(01) dStSt = rmiddotdt + smiddotdWt
GARCH SVM (Mean-Reverting Process)
Ri = μ+σiεi εi ~ N(01)
σi 2 = α0+Σp
j=1αj εi-j2 +Σq
j=1βj σ i-j2
dStSt = rmiddotdt + |Vt|middotdWt
dVt = -kmiddot(Vt-c)middotdt + f(Vt)dZt
Generalization Generalization
Ri = μ(Ri-1 Ri-2 hellip)+σ (Ri-1 Ri-2 hellip) εi dStSt = Mtmiddotdt + VtmiddotdWt
could the models borrowed from physical systems well approach econ ones
Finding Clues for
Verifying Models
just simply a normal distributionor
a complicated mixture of normal distributions
tractable Dynamic Structure out there
dynamic tracingstatic de-mixing
bull Strength ndash Formulation amp Correction about Dynamic Structure
strong probabilistic formulation for
consistent strategy construction by risk-return trade-off and
systematic risk management (tools amp paradigms by financial engineering)
bull Weakness ndash Observation amp Explanation about Dynamic Phenomena
Ignoring (if any) ldquocyclic phenomenardquo and ldquoinvestment paradigmsrdquodue to
market demand-supply mechanism driven by
market sentiment and rationality
Strength and Weakness of
Stochastic-Process Modeling
be aware of simple biases
Part III
Reality amp
Lessons
itrsquos a jungle out there
bull Capital Markets are Complex Dynamic Systemsbull Non-linear Dynamic Mechanismbull Non-stationary Evolution due to changing Econ Conditions and Investment Paradigms
bull Multi-Component Framework of Market Behaviorbull Trend ndash Change Points Long-Term Evolutionary Structural Changesbull Seasonality ndash Periodic Factors bull Cycles ndash Dynamic Swings around Equilibriumbull Shocks ndash Unpredictable Impactsbull Noises ndash Endogenous and Environmental Uncertainties
bull Diversification in Market Constitutionbull Sentiment ndash Individual Investorsbull Rationality ndash Institutional Investors (Smart Money)bull Strategy ndash Arbitrageurs Risk Hedgers
bull Multi-Channel Infrastructure of Money Flowsbull Swifter and Swifter Trading Systemsbull Broader and Broader Asset Categoriesbull More Sophisticated and Complicated Financial Products and Trading Schemes
bull Reflexivity
The Complex Reality for
Thoughts
too many factors affecting market movements to figure out
can
deal with it
GARCH
Multi-Resolutionof
Complex Market Time Series
wavelet-based decomposition to figure out market behavior features
1974 Great Stock Market Capitulation
1987 Great Stock Market Crash
1989 Nikkei Bubble Burst
1997 Asian Currency Crisis
1998 LTCM Fallout
2000 Nasdaq (Tech) Bubble Burst
Hard Lessons from
Markets
dynamic risks beyond interpretation of stochastic volatility (no anomaly talk)
Part IV
Rational Memory Processes
a canonical methodological frameworkof
capital market modeling based on
financial signal processing
bull Theoretical Issues (about mathematical analysis)bull Dynamics ndash Demand Supply Mechanism
bull Randomness ndash Uncertainty Structure (multi-scale noise structure)
bull Practical Issues (about paradigms)bull Market Sentiment ndash Momentum Uncertainty
bull Market Rationality ndash Prediction Risk-Return Trade-Off
bull Market Strategy ndash Arbitrage Risk Hedging Schemes
bull Market Efficiency amp Completeness ndash Financial Infrastructures Products
bull Market Liquidity amp Friction ndash Trading Volumes Cost Turn-Over rate
bull Market Constitution ndash Economical Cultural Geopolitical Backgrounds
bull Technical Issues (about applications and implications)bull Model Identification ndash Parameter Estimation
bull Model Assessment ndash Modeling Risk (Modeling Bias Estimation Loss)
bull Model Adaptation ndash Coefficient Relations to Econ and Other Marketsrsquo Conditions
bull Model Extensibility ndash Extension to Absorb New Factors counting for ldquoAnomaliesrdquo
Prospects for
Modeling Capital Markets
setting a modeling methodological framework to incorporate the prospects
Challenges for
Modeling Capital Markets
bull Non-linearity amp Non-stationarity in Signal Dynamics
bull Complexity in Signal Structure
bull Noise Barrier (Overwhelming Noise-to-Signal Ratio)
bull Nonparametric Estimation (MLE does not make sense anymore here)
Curse of Dimensionality
1 2 3 4 5 6 7 8 9 10 11 12
Piecewise (Monthly) Constant Geometric Brownian Motion
Ri = μ(Ri-1 Ri-2 hellip)+σ (Ri-1 Ri-2 hellip) εi
Technical Foundationfor
Financial Signal Processing
Transformation Magic to break Curse of Dimensionality
Analyzing Signals over Fourier Frequency Domain
Analyzing Signals in Wavelet Multi-Resolution Framework
Complexity in Signal Structure
Non-linearity amp Non-stationarity in Signal Dynamics
Analyzing Signals over Dynamic Domain
in
Wavelet Multi-Resolution Framework
Fundamental Signal Processing Tasksfor
Financial Engineering
an objective way to format market patterns from experience
FilterHistoric
Time SeriesTechnicalIndicator
DiS0 S1 hellip Si
Di =Г(S0 hellip Si V0 hellip Vi |өi)
Dt =Гt(Sτ[0t])continuous-time approach
special interested format
Di =Г(R1 hellip Ri) Rj = (Sj-Sj-1)Sj-1
linear stationary case
Di = c1middotR1 + hellip + cimiddotRi Dt = int[0t]k(|τ-t|)middotSτ-1dSτ
Examples of
Dynamic Indicators
Dancing with Cycles
0 100 200 300 400 500 600 700-5
-4
-3
-2
-1
0
1
2
3
4
5
121951 022003
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
Dynamic Indicators Technical Indicators which serve to monitor and gauge market cycles
Critical Patternsof
Long-Term Cyclic Phenomena
0 50 100 150-2
-1
0
1
2
3
4
Jul 1993
Oct 1987
Nov 1981
Feb 1986
MaxUncertaintyLine
12-Month STTB Moving Average 12-Month SampP500 Return MA ()
Principle of Cyclic Hazard
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
1285 1290 0496
0401
Nikkei 225 SampP 500
TAIEX
Example Iof
Short-Horizon Dynamic Patterns
catching rebounding points and finding implicit trend forces
Fidelity Emerging Markets Fund (USD)
Fidelity Technology Fund (EUR) Fidelity American Growth Fund (USD)
Fidelity World Fund (EUR)
08182003 0120204 08182003 0120204
08182003 0120204 08182003 0120204
Index Value
20-Day STTB
Example IIof
Short-Horizon Dynamic Patterns
catching a rebounding and surging point
20-Day STTB
Example IIIof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Currency Triangular Arbitraging
12-Month MA of USD-vs-EUR Return Rate
12-Month MA of USD-vs-JPY Return Rate
12-Month MA of USD-vs-EUR 12-M STTB
12-Month MA of USD-vs-JPY 12-M STTB
Example IVof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Stock-Index Triangular Arbitraging
02132003 01162004
TWSEBKITWSE Cumulative Relative Return Rate (3)
TWSEELECTWSE Cumulative Relative Return Rate (3)
5-Day MA of TWSEBKITWSE Relative 20-Day STTB
5-Day MA of TWSEELECTWSE Relative 20-Day STTB
bull Physical Meanings - indicating practical market sense eg momentum uncertainty stability liquidity hellip etc
bull Cycle-Leading
bull Consistency amp Universality (Time amp Geography)
Conditionsof
Modeling Potential
warning markets might have no real intentions but filtersrsquo illusions
0 10 20 30 40 50 60-2
-1
0
1
2
3
4
011981 061985
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
- eg
Constructing Indicator-Oriented Strategieswith or without
Modeling
from empirical to theoretical
0 05 1 15 2 25 3 35 4-2
0
2
4
6
8
10H i+1
Si
Empirical Raw Optimal Strategy Theoretical Raw Optimal Strategy ΨΣ2
Methodological Framework of
Modeling Capital Markets
dynamics based on rationality oriented by memory filtered by dynamic kernel
Rational Memory Process
Ri+1-ri = Ψө(Di) + Ση(Di)middotεi+1
continuous-time approach (with a linear stationary filter)
dStSt = Ψө(int[0t]k(|τ-t|)middotSτ-1dSτ) middotdt + Ση(int[0t]k(|τ-t|)middotSτ
-1dSτ)middotdWt
Market Aggregation Rationality
Market Background Conditions
bull neatly constructing dynamic investment strategies on the dynamic domain
bull analytic calculation of risk-return trade-off curve via calculus of variation
bull easily formulating integrated-volatility for simulating risk-neutral probability density and calculating VaR
bull turning nonlinear dynamic auto-regression into static nonparametric regression
bull introducing adaptive statistical estimation methods to separate stationary and non-stationary factors
bull assessing modeling risk
bull paving a way to ldquostatistical financerdquo (market energy)
bull keeping the modeling framework flexible and adaptive under reflexivity
bull pricing profitable financial knowledges based on valuable dynamic kernels
Advantages on
Dynamic Domain
building robust amp adaptive models for financial engineering in magic domains
Finding Clues for
Verifying Models
just simply a normal distributionor
a complicated mixture of normal distributions
tractable Dynamic Structure out there
dynamic tracingstatic de-mixing
bull Strength ndash Formulation amp Correction about Dynamic Structure
strong probabilistic formulation for
consistent strategy construction by risk-return trade-off and
systematic risk management (tools amp paradigms by financial engineering)
bull Weakness ndash Observation amp Explanation about Dynamic Phenomena
Ignoring (if any) ldquocyclic phenomenardquo and ldquoinvestment paradigmsrdquodue to
market demand-supply mechanism driven by
market sentiment and rationality
Strength and Weakness of
Stochastic-Process Modeling
be aware of simple biases
Part III
Reality amp
Lessons
itrsquos a jungle out there
bull Capital Markets are Complex Dynamic Systemsbull Non-linear Dynamic Mechanismbull Non-stationary Evolution due to changing Econ Conditions and Investment Paradigms
bull Multi-Component Framework of Market Behaviorbull Trend ndash Change Points Long-Term Evolutionary Structural Changesbull Seasonality ndash Periodic Factors bull Cycles ndash Dynamic Swings around Equilibriumbull Shocks ndash Unpredictable Impactsbull Noises ndash Endogenous and Environmental Uncertainties
bull Diversification in Market Constitutionbull Sentiment ndash Individual Investorsbull Rationality ndash Institutional Investors (Smart Money)bull Strategy ndash Arbitrageurs Risk Hedgers
bull Multi-Channel Infrastructure of Money Flowsbull Swifter and Swifter Trading Systemsbull Broader and Broader Asset Categoriesbull More Sophisticated and Complicated Financial Products and Trading Schemes
bull Reflexivity
The Complex Reality for
Thoughts
too many factors affecting market movements to figure out
can
deal with it
GARCH
Multi-Resolutionof
Complex Market Time Series
wavelet-based decomposition to figure out market behavior features
1974 Great Stock Market Capitulation
1987 Great Stock Market Crash
1989 Nikkei Bubble Burst
1997 Asian Currency Crisis
1998 LTCM Fallout
2000 Nasdaq (Tech) Bubble Burst
Hard Lessons from
Markets
dynamic risks beyond interpretation of stochastic volatility (no anomaly talk)
Part IV
Rational Memory Processes
a canonical methodological frameworkof
capital market modeling based on
financial signal processing
bull Theoretical Issues (about mathematical analysis)bull Dynamics ndash Demand Supply Mechanism
bull Randomness ndash Uncertainty Structure (multi-scale noise structure)
bull Practical Issues (about paradigms)bull Market Sentiment ndash Momentum Uncertainty
bull Market Rationality ndash Prediction Risk-Return Trade-Off
bull Market Strategy ndash Arbitrage Risk Hedging Schemes
bull Market Efficiency amp Completeness ndash Financial Infrastructures Products
bull Market Liquidity amp Friction ndash Trading Volumes Cost Turn-Over rate
bull Market Constitution ndash Economical Cultural Geopolitical Backgrounds
bull Technical Issues (about applications and implications)bull Model Identification ndash Parameter Estimation
bull Model Assessment ndash Modeling Risk (Modeling Bias Estimation Loss)
bull Model Adaptation ndash Coefficient Relations to Econ and Other Marketsrsquo Conditions
bull Model Extensibility ndash Extension to Absorb New Factors counting for ldquoAnomaliesrdquo
Prospects for
Modeling Capital Markets
setting a modeling methodological framework to incorporate the prospects
Challenges for
Modeling Capital Markets
bull Non-linearity amp Non-stationarity in Signal Dynamics
bull Complexity in Signal Structure
bull Noise Barrier (Overwhelming Noise-to-Signal Ratio)
bull Nonparametric Estimation (MLE does not make sense anymore here)
Curse of Dimensionality
1 2 3 4 5 6 7 8 9 10 11 12
Piecewise (Monthly) Constant Geometric Brownian Motion
Ri = μ(Ri-1 Ri-2 hellip)+σ (Ri-1 Ri-2 hellip) εi
Technical Foundationfor
Financial Signal Processing
Transformation Magic to break Curse of Dimensionality
Analyzing Signals over Fourier Frequency Domain
Analyzing Signals in Wavelet Multi-Resolution Framework
Complexity in Signal Structure
Non-linearity amp Non-stationarity in Signal Dynamics
Analyzing Signals over Dynamic Domain
in
Wavelet Multi-Resolution Framework
Fundamental Signal Processing Tasksfor
Financial Engineering
an objective way to format market patterns from experience
FilterHistoric
Time SeriesTechnicalIndicator
DiS0 S1 hellip Si
Di =Г(S0 hellip Si V0 hellip Vi |өi)
Dt =Гt(Sτ[0t])continuous-time approach
special interested format
Di =Г(R1 hellip Ri) Rj = (Sj-Sj-1)Sj-1
linear stationary case
Di = c1middotR1 + hellip + cimiddotRi Dt = int[0t]k(|τ-t|)middotSτ-1dSτ
Examples of
Dynamic Indicators
Dancing with Cycles
0 100 200 300 400 500 600 700-5
-4
-3
-2
-1
0
1
2
3
4
5
121951 022003
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
Dynamic Indicators Technical Indicators which serve to monitor and gauge market cycles
Critical Patternsof
Long-Term Cyclic Phenomena
0 50 100 150-2
-1
0
1
2
3
4
Jul 1993
Oct 1987
Nov 1981
Feb 1986
MaxUncertaintyLine
12-Month STTB Moving Average 12-Month SampP500 Return MA ()
Principle of Cyclic Hazard
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
1285 1290 0496
0401
Nikkei 225 SampP 500
TAIEX
Example Iof
Short-Horizon Dynamic Patterns
catching rebounding points and finding implicit trend forces
Fidelity Emerging Markets Fund (USD)
Fidelity Technology Fund (EUR) Fidelity American Growth Fund (USD)
Fidelity World Fund (EUR)
08182003 0120204 08182003 0120204
08182003 0120204 08182003 0120204
Index Value
20-Day STTB
Example IIof
Short-Horizon Dynamic Patterns
catching a rebounding and surging point
20-Day STTB
Example IIIof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Currency Triangular Arbitraging
12-Month MA of USD-vs-EUR Return Rate
12-Month MA of USD-vs-JPY Return Rate
12-Month MA of USD-vs-EUR 12-M STTB
12-Month MA of USD-vs-JPY 12-M STTB
Example IVof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Stock-Index Triangular Arbitraging
02132003 01162004
TWSEBKITWSE Cumulative Relative Return Rate (3)
TWSEELECTWSE Cumulative Relative Return Rate (3)
5-Day MA of TWSEBKITWSE Relative 20-Day STTB
5-Day MA of TWSEELECTWSE Relative 20-Day STTB
bull Physical Meanings - indicating practical market sense eg momentum uncertainty stability liquidity hellip etc
bull Cycle-Leading
bull Consistency amp Universality (Time amp Geography)
Conditionsof
Modeling Potential
warning markets might have no real intentions but filtersrsquo illusions
0 10 20 30 40 50 60-2
-1
0
1
2
3
4
011981 061985
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
- eg
Constructing Indicator-Oriented Strategieswith or without
Modeling
from empirical to theoretical
0 05 1 15 2 25 3 35 4-2
0
2
4
6
8
10H i+1
Si
Empirical Raw Optimal Strategy Theoretical Raw Optimal Strategy ΨΣ2
Methodological Framework of
Modeling Capital Markets
dynamics based on rationality oriented by memory filtered by dynamic kernel
Rational Memory Process
Ri+1-ri = Ψө(Di) + Ση(Di)middotεi+1
continuous-time approach (with a linear stationary filter)
dStSt = Ψө(int[0t]k(|τ-t|)middotSτ-1dSτ) middotdt + Ση(int[0t]k(|τ-t|)middotSτ
-1dSτ)middotdWt
Market Aggregation Rationality
Market Background Conditions
bull neatly constructing dynamic investment strategies on the dynamic domain
bull analytic calculation of risk-return trade-off curve via calculus of variation
bull easily formulating integrated-volatility for simulating risk-neutral probability density and calculating VaR
bull turning nonlinear dynamic auto-regression into static nonparametric regression
bull introducing adaptive statistical estimation methods to separate stationary and non-stationary factors
bull assessing modeling risk
bull paving a way to ldquostatistical financerdquo (market energy)
bull keeping the modeling framework flexible and adaptive under reflexivity
bull pricing profitable financial knowledges based on valuable dynamic kernels
Advantages on
Dynamic Domain
building robust amp adaptive models for financial engineering in magic domains
bull Strength ndash Formulation amp Correction about Dynamic Structure
strong probabilistic formulation for
consistent strategy construction by risk-return trade-off and
systematic risk management (tools amp paradigms by financial engineering)
bull Weakness ndash Observation amp Explanation about Dynamic Phenomena
Ignoring (if any) ldquocyclic phenomenardquo and ldquoinvestment paradigmsrdquodue to
market demand-supply mechanism driven by
market sentiment and rationality
Strength and Weakness of
Stochastic-Process Modeling
be aware of simple biases
Part III
Reality amp
Lessons
itrsquos a jungle out there
bull Capital Markets are Complex Dynamic Systemsbull Non-linear Dynamic Mechanismbull Non-stationary Evolution due to changing Econ Conditions and Investment Paradigms
bull Multi-Component Framework of Market Behaviorbull Trend ndash Change Points Long-Term Evolutionary Structural Changesbull Seasonality ndash Periodic Factors bull Cycles ndash Dynamic Swings around Equilibriumbull Shocks ndash Unpredictable Impactsbull Noises ndash Endogenous and Environmental Uncertainties
bull Diversification in Market Constitutionbull Sentiment ndash Individual Investorsbull Rationality ndash Institutional Investors (Smart Money)bull Strategy ndash Arbitrageurs Risk Hedgers
bull Multi-Channel Infrastructure of Money Flowsbull Swifter and Swifter Trading Systemsbull Broader and Broader Asset Categoriesbull More Sophisticated and Complicated Financial Products and Trading Schemes
bull Reflexivity
The Complex Reality for
Thoughts
too many factors affecting market movements to figure out
can
deal with it
GARCH
Multi-Resolutionof
Complex Market Time Series
wavelet-based decomposition to figure out market behavior features
1974 Great Stock Market Capitulation
1987 Great Stock Market Crash
1989 Nikkei Bubble Burst
1997 Asian Currency Crisis
1998 LTCM Fallout
2000 Nasdaq (Tech) Bubble Burst
Hard Lessons from
Markets
dynamic risks beyond interpretation of stochastic volatility (no anomaly talk)
Part IV
Rational Memory Processes
a canonical methodological frameworkof
capital market modeling based on
financial signal processing
bull Theoretical Issues (about mathematical analysis)bull Dynamics ndash Demand Supply Mechanism
bull Randomness ndash Uncertainty Structure (multi-scale noise structure)
bull Practical Issues (about paradigms)bull Market Sentiment ndash Momentum Uncertainty
bull Market Rationality ndash Prediction Risk-Return Trade-Off
bull Market Strategy ndash Arbitrage Risk Hedging Schemes
bull Market Efficiency amp Completeness ndash Financial Infrastructures Products
bull Market Liquidity amp Friction ndash Trading Volumes Cost Turn-Over rate
bull Market Constitution ndash Economical Cultural Geopolitical Backgrounds
bull Technical Issues (about applications and implications)bull Model Identification ndash Parameter Estimation
bull Model Assessment ndash Modeling Risk (Modeling Bias Estimation Loss)
bull Model Adaptation ndash Coefficient Relations to Econ and Other Marketsrsquo Conditions
bull Model Extensibility ndash Extension to Absorb New Factors counting for ldquoAnomaliesrdquo
Prospects for
Modeling Capital Markets
setting a modeling methodological framework to incorporate the prospects
Challenges for
Modeling Capital Markets
bull Non-linearity amp Non-stationarity in Signal Dynamics
bull Complexity in Signal Structure
bull Noise Barrier (Overwhelming Noise-to-Signal Ratio)
bull Nonparametric Estimation (MLE does not make sense anymore here)
Curse of Dimensionality
1 2 3 4 5 6 7 8 9 10 11 12
Piecewise (Monthly) Constant Geometric Brownian Motion
Ri = μ(Ri-1 Ri-2 hellip)+σ (Ri-1 Ri-2 hellip) εi
Technical Foundationfor
Financial Signal Processing
Transformation Magic to break Curse of Dimensionality
Analyzing Signals over Fourier Frequency Domain
Analyzing Signals in Wavelet Multi-Resolution Framework
Complexity in Signal Structure
Non-linearity amp Non-stationarity in Signal Dynamics
Analyzing Signals over Dynamic Domain
in
Wavelet Multi-Resolution Framework
Fundamental Signal Processing Tasksfor
Financial Engineering
an objective way to format market patterns from experience
FilterHistoric
Time SeriesTechnicalIndicator
DiS0 S1 hellip Si
Di =Г(S0 hellip Si V0 hellip Vi |өi)
Dt =Гt(Sτ[0t])continuous-time approach
special interested format
Di =Г(R1 hellip Ri) Rj = (Sj-Sj-1)Sj-1
linear stationary case
Di = c1middotR1 + hellip + cimiddotRi Dt = int[0t]k(|τ-t|)middotSτ-1dSτ
Examples of
Dynamic Indicators
Dancing with Cycles
0 100 200 300 400 500 600 700-5
-4
-3
-2
-1
0
1
2
3
4
5
121951 022003
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
Dynamic Indicators Technical Indicators which serve to monitor and gauge market cycles
Critical Patternsof
Long-Term Cyclic Phenomena
0 50 100 150-2
-1
0
1
2
3
4
Jul 1993
Oct 1987
Nov 1981
Feb 1986
MaxUncertaintyLine
12-Month STTB Moving Average 12-Month SampP500 Return MA ()
Principle of Cyclic Hazard
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
1285 1290 0496
0401
Nikkei 225 SampP 500
TAIEX
Example Iof
Short-Horizon Dynamic Patterns
catching rebounding points and finding implicit trend forces
Fidelity Emerging Markets Fund (USD)
Fidelity Technology Fund (EUR) Fidelity American Growth Fund (USD)
Fidelity World Fund (EUR)
08182003 0120204 08182003 0120204
08182003 0120204 08182003 0120204
Index Value
20-Day STTB
Example IIof
Short-Horizon Dynamic Patterns
catching a rebounding and surging point
20-Day STTB
Example IIIof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Currency Triangular Arbitraging
12-Month MA of USD-vs-EUR Return Rate
12-Month MA of USD-vs-JPY Return Rate
12-Month MA of USD-vs-EUR 12-M STTB
12-Month MA of USD-vs-JPY 12-M STTB
Example IVof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Stock-Index Triangular Arbitraging
02132003 01162004
TWSEBKITWSE Cumulative Relative Return Rate (3)
TWSEELECTWSE Cumulative Relative Return Rate (3)
5-Day MA of TWSEBKITWSE Relative 20-Day STTB
5-Day MA of TWSEELECTWSE Relative 20-Day STTB
bull Physical Meanings - indicating practical market sense eg momentum uncertainty stability liquidity hellip etc
bull Cycle-Leading
bull Consistency amp Universality (Time amp Geography)
Conditionsof
Modeling Potential
warning markets might have no real intentions but filtersrsquo illusions
0 10 20 30 40 50 60-2
-1
0
1
2
3
4
011981 061985
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
- eg
Constructing Indicator-Oriented Strategieswith or without
Modeling
from empirical to theoretical
0 05 1 15 2 25 3 35 4-2
0
2
4
6
8
10H i+1
Si
Empirical Raw Optimal Strategy Theoretical Raw Optimal Strategy ΨΣ2
Methodological Framework of
Modeling Capital Markets
dynamics based on rationality oriented by memory filtered by dynamic kernel
Rational Memory Process
Ri+1-ri = Ψө(Di) + Ση(Di)middotεi+1
continuous-time approach (with a linear stationary filter)
dStSt = Ψө(int[0t]k(|τ-t|)middotSτ-1dSτ) middotdt + Ση(int[0t]k(|τ-t|)middotSτ
-1dSτ)middotdWt
Market Aggregation Rationality
Market Background Conditions
bull neatly constructing dynamic investment strategies on the dynamic domain
bull analytic calculation of risk-return trade-off curve via calculus of variation
bull easily formulating integrated-volatility for simulating risk-neutral probability density and calculating VaR
bull turning nonlinear dynamic auto-regression into static nonparametric regression
bull introducing adaptive statistical estimation methods to separate stationary and non-stationary factors
bull assessing modeling risk
bull paving a way to ldquostatistical financerdquo (market energy)
bull keeping the modeling framework flexible and adaptive under reflexivity
bull pricing profitable financial knowledges based on valuable dynamic kernels
Advantages on
Dynamic Domain
building robust amp adaptive models for financial engineering in magic domains
Part III
Reality amp
Lessons
itrsquos a jungle out there
bull Capital Markets are Complex Dynamic Systemsbull Non-linear Dynamic Mechanismbull Non-stationary Evolution due to changing Econ Conditions and Investment Paradigms
bull Multi-Component Framework of Market Behaviorbull Trend ndash Change Points Long-Term Evolutionary Structural Changesbull Seasonality ndash Periodic Factors bull Cycles ndash Dynamic Swings around Equilibriumbull Shocks ndash Unpredictable Impactsbull Noises ndash Endogenous and Environmental Uncertainties
bull Diversification in Market Constitutionbull Sentiment ndash Individual Investorsbull Rationality ndash Institutional Investors (Smart Money)bull Strategy ndash Arbitrageurs Risk Hedgers
bull Multi-Channel Infrastructure of Money Flowsbull Swifter and Swifter Trading Systemsbull Broader and Broader Asset Categoriesbull More Sophisticated and Complicated Financial Products and Trading Schemes
bull Reflexivity
The Complex Reality for
Thoughts
too many factors affecting market movements to figure out
can
deal with it
GARCH
Multi-Resolutionof
Complex Market Time Series
wavelet-based decomposition to figure out market behavior features
1974 Great Stock Market Capitulation
1987 Great Stock Market Crash
1989 Nikkei Bubble Burst
1997 Asian Currency Crisis
1998 LTCM Fallout
2000 Nasdaq (Tech) Bubble Burst
Hard Lessons from
Markets
dynamic risks beyond interpretation of stochastic volatility (no anomaly talk)
Part IV
Rational Memory Processes
a canonical methodological frameworkof
capital market modeling based on
financial signal processing
bull Theoretical Issues (about mathematical analysis)bull Dynamics ndash Demand Supply Mechanism
bull Randomness ndash Uncertainty Structure (multi-scale noise structure)
bull Practical Issues (about paradigms)bull Market Sentiment ndash Momentum Uncertainty
bull Market Rationality ndash Prediction Risk-Return Trade-Off
bull Market Strategy ndash Arbitrage Risk Hedging Schemes
bull Market Efficiency amp Completeness ndash Financial Infrastructures Products
bull Market Liquidity amp Friction ndash Trading Volumes Cost Turn-Over rate
bull Market Constitution ndash Economical Cultural Geopolitical Backgrounds
bull Technical Issues (about applications and implications)bull Model Identification ndash Parameter Estimation
bull Model Assessment ndash Modeling Risk (Modeling Bias Estimation Loss)
bull Model Adaptation ndash Coefficient Relations to Econ and Other Marketsrsquo Conditions
bull Model Extensibility ndash Extension to Absorb New Factors counting for ldquoAnomaliesrdquo
Prospects for
Modeling Capital Markets
setting a modeling methodological framework to incorporate the prospects
Challenges for
Modeling Capital Markets
bull Non-linearity amp Non-stationarity in Signal Dynamics
bull Complexity in Signal Structure
bull Noise Barrier (Overwhelming Noise-to-Signal Ratio)
bull Nonparametric Estimation (MLE does not make sense anymore here)
Curse of Dimensionality
1 2 3 4 5 6 7 8 9 10 11 12
Piecewise (Monthly) Constant Geometric Brownian Motion
Ri = μ(Ri-1 Ri-2 hellip)+σ (Ri-1 Ri-2 hellip) εi
Technical Foundationfor
Financial Signal Processing
Transformation Magic to break Curse of Dimensionality
Analyzing Signals over Fourier Frequency Domain
Analyzing Signals in Wavelet Multi-Resolution Framework
Complexity in Signal Structure
Non-linearity amp Non-stationarity in Signal Dynamics
Analyzing Signals over Dynamic Domain
in
Wavelet Multi-Resolution Framework
Fundamental Signal Processing Tasksfor
Financial Engineering
an objective way to format market patterns from experience
FilterHistoric
Time SeriesTechnicalIndicator
DiS0 S1 hellip Si
Di =Г(S0 hellip Si V0 hellip Vi |өi)
Dt =Гt(Sτ[0t])continuous-time approach
special interested format
Di =Г(R1 hellip Ri) Rj = (Sj-Sj-1)Sj-1
linear stationary case
Di = c1middotR1 + hellip + cimiddotRi Dt = int[0t]k(|τ-t|)middotSτ-1dSτ
Examples of
Dynamic Indicators
Dancing with Cycles
0 100 200 300 400 500 600 700-5
-4
-3
-2
-1
0
1
2
3
4
5
121951 022003
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
Dynamic Indicators Technical Indicators which serve to monitor and gauge market cycles
Critical Patternsof
Long-Term Cyclic Phenomena
0 50 100 150-2
-1
0
1
2
3
4
Jul 1993
Oct 1987
Nov 1981
Feb 1986
MaxUncertaintyLine
12-Month STTB Moving Average 12-Month SampP500 Return MA ()
Principle of Cyclic Hazard
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
1285 1290 0496
0401
Nikkei 225 SampP 500
TAIEX
Example Iof
Short-Horizon Dynamic Patterns
catching rebounding points and finding implicit trend forces
Fidelity Emerging Markets Fund (USD)
Fidelity Technology Fund (EUR) Fidelity American Growth Fund (USD)
Fidelity World Fund (EUR)
08182003 0120204 08182003 0120204
08182003 0120204 08182003 0120204
Index Value
20-Day STTB
Example IIof
Short-Horizon Dynamic Patterns
catching a rebounding and surging point
20-Day STTB
Example IIIof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Currency Triangular Arbitraging
12-Month MA of USD-vs-EUR Return Rate
12-Month MA of USD-vs-JPY Return Rate
12-Month MA of USD-vs-EUR 12-M STTB
12-Month MA of USD-vs-JPY 12-M STTB
Example IVof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Stock-Index Triangular Arbitraging
02132003 01162004
TWSEBKITWSE Cumulative Relative Return Rate (3)
TWSEELECTWSE Cumulative Relative Return Rate (3)
5-Day MA of TWSEBKITWSE Relative 20-Day STTB
5-Day MA of TWSEELECTWSE Relative 20-Day STTB
bull Physical Meanings - indicating practical market sense eg momentum uncertainty stability liquidity hellip etc
bull Cycle-Leading
bull Consistency amp Universality (Time amp Geography)
Conditionsof
Modeling Potential
warning markets might have no real intentions but filtersrsquo illusions
0 10 20 30 40 50 60-2
-1
0
1
2
3
4
011981 061985
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
- eg
Constructing Indicator-Oriented Strategieswith or without
Modeling
from empirical to theoretical
0 05 1 15 2 25 3 35 4-2
0
2
4
6
8
10H i+1
Si
Empirical Raw Optimal Strategy Theoretical Raw Optimal Strategy ΨΣ2
Methodological Framework of
Modeling Capital Markets
dynamics based on rationality oriented by memory filtered by dynamic kernel
Rational Memory Process
Ri+1-ri = Ψө(Di) + Ση(Di)middotεi+1
continuous-time approach (with a linear stationary filter)
dStSt = Ψө(int[0t]k(|τ-t|)middotSτ-1dSτ) middotdt + Ση(int[0t]k(|τ-t|)middotSτ
-1dSτ)middotdWt
Market Aggregation Rationality
Market Background Conditions
bull neatly constructing dynamic investment strategies on the dynamic domain
bull analytic calculation of risk-return trade-off curve via calculus of variation
bull easily formulating integrated-volatility for simulating risk-neutral probability density and calculating VaR
bull turning nonlinear dynamic auto-regression into static nonparametric regression
bull introducing adaptive statistical estimation methods to separate stationary and non-stationary factors
bull assessing modeling risk
bull paving a way to ldquostatistical financerdquo (market energy)
bull keeping the modeling framework flexible and adaptive under reflexivity
bull pricing profitable financial knowledges based on valuable dynamic kernels
Advantages on
Dynamic Domain
building robust amp adaptive models for financial engineering in magic domains
bull Capital Markets are Complex Dynamic Systemsbull Non-linear Dynamic Mechanismbull Non-stationary Evolution due to changing Econ Conditions and Investment Paradigms
bull Multi-Component Framework of Market Behaviorbull Trend ndash Change Points Long-Term Evolutionary Structural Changesbull Seasonality ndash Periodic Factors bull Cycles ndash Dynamic Swings around Equilibriumbull Shocks ndash Unpredictable Impactsbull Noises ndash Endogenous and Environmental Uncertainties
bull Diversification in Market Constitutionbull Sentiment ndash Individual Investorsbull Rationality ndash Institutional Investors (Smart Money)bull Strategy ndash Arbitrageurs Risk Hedgers
bull Multi-Channel Infrastructure of Money Flowsbull Swifter and Swifter Trading Systemsbull Broader and Broader Asset Categoriesbull More Sophisticated and Complicated Financial Products and Trading Schemes
bull Reflexivity
The Complex Reality for
Thoughts
too many factors affecting market movements to figure out
can
deal with it
GARCH
Multi-Resolutionof
Complex Market Time Series
wavelet-based decomposition to figure out market behavior features
1974 Great Stock Market Capitulation
1987 Great Stock Market Crash
1989 Nikkei Bubble Burst
1997 Asian Currency Crisis
1998 LTCM Fallout
2000 Nasdaq (Tech) Bubble Burst
Hard Lessons from
Markets
dynamic risks beyond interpretation of stochastic volatility (no anomaly talk)
Part IV
Rational Memory Processes
a canonical methodological frameworkof
capital market modeling based on
financial signal processing
bull Theoretical Issues (about mathematical analysis)bull Dynamics ndash Demand Supply Mechanism
bull Randomness ndash Uncertainty Structure (multi-scale noise structure)
bull Practical Issues (about paradigms)bull Market Sentiment ndash Momentum Uncertainty
bull Market Rationality ndash Prediction Risk-Return Trade-Off
bull Market Strategy ndash Arbitrage Risk Hedging Schemes
bull Market Efficiency amp Completeness ndash Financial Infrastructures Products
bull Market Liquidity amp Friction ndash Trading Volumes Cost Turn-Over rate
bull Market Constitution ndash Economical Cultural Geopolitical Backgrounds
bull Technical Issues (about applications and implications)bull Model Identification ndash Parameter Estimation
bull Model Assessment ndash Modeling Risk (Modeling Bias Estimation Loss)
bull Model Adaptation ndash Coefficient Relations to Econ and Other Marketsrsquo Conditions
bull Model Extensibility ndash Extension to Absorb New Factors counting for ldquoAnomaliesrdquo
Prospects for
Modeling Capital Markets
setting a modeling methodological framework to incorporate the prospects
Challenges for
Modeling Capital Markets
bull Non-linearity amp Non-stationarity in Signal Dynamics
bull Complexity in Signal Structure
bull Noise Barrier (Overwhelming Noise-to-Signal Ratio)
bull Nonparametric Estimation (MLE does not make sense anymore here)
Curse of Dimensionality
1 2 3 4 5 6 7 8 9 10 11 12
Piecewise (Monthly) Constant Geometric Brownian Motion
Ri = μ(Ri-1 Ri-2 hellip)+σ (Ri-1 Ri-2 hellip) εi
Technical Foundationfor
Financial Signal Processing
Transformation Magic to break Curse of Dimensionality
Analyzing Signals over Fourier Frequency Domain
Analyzing Signals in Wavelet Multi-Resolution Framework
Complexity in Signal Structure
Non-linearity amp Non-stationarity in Signal Dynamics
Analyzing Signals over Dynamic Domain
in
Wavelet Multi-Resolution Framework
Fundamental Signal Processing Tasksfor
Financial Engineering
an objective way to format market patterns from experience
FilterHistoric
Time SeriesTechnicalIndicator
DiS0 S1 hellip Si
Di =Г(S0 hellip Si V0 hellip Vi |өi)
Dt =Гt(Sτ[0t])continuous-time approach
special interested format
Di =Г(R1 hellip Ri) Rj = (Sj-Sj-1)Sj-1
linear stationary case
Di = c1middotR1 + hellip + cimiddotRi Dt = int[0t]k(|τ-t|)middotSτ-1dSτ
Examples of
Dynamic Indicators
Dancing with Cycles
0 100 200 300 400 500 600 700-5
-4
-3
-2
-1
0
1
2
3
4
5
121951 022003
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
Dynamic Indicators Technical Indicators which serve to monitor and gauge market cycles
Critical Patternsof
Long-Term Cyclic Phenomena
0 50 100 150-2
-1
0
1
2
3
4
Jul 1993
Oct 1987
Nov 1981
Feb 1986
MaxUncertaintyLine
12-Month STTB Moving Average 12-Month SampP500 Return MA ()
Principle of Cyclic Hazard
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
1285 1290 0496
0401
Nikkei 225 SampP 500
TAIEX
Example Iof
Short-Horizon Dynamic Patterns
catching rebounding points and finding implicit trend forces
Fidelity Emerging Markets Fund (USD)
Fidelity Technology Fund (EUR) Fidelity American Growth Fund (USD)
Fidelity World Fund (EUR)
08182003 0120204 08182003 0120204
08182003 0120204 08182003 0120204
Index Value
20-Day STTB
Example IIof
Short-Horizon Dynamic Patterns
catching a rebounding and surging point
20-Day STTB
Example IIIof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Currency Triangular Arbitraging
12-Month MA of USD-vs-EUR Return Rate
12-Month MA of USD-vs-JPY Return Rate
12-Month MA of USD-vs-EUR 12-M STTB
12-Month MA of USD-vs-JPY 12-M STTB
Example IVof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Stock-Index Triangular Arbitraging
02132003 01162004
TWSEBKITWSE Cumulative Relative Return Rate (3)
TWSEELECTWSE Cumulative Relative Return Rate (3)
5-Day MA of TWSEBKITWSE Relative 20-Day STTB
5-Day MA of TWSEELECTWSE Relative 20-Day STTB
bull Physical Meanings - indicating practical market sense eg momentum uncertainty stability liquidity hellip etc
bull Cycle-Leading
bull Consistency amp Universality (Time amp Geography)
Conditionsof
Modeling Potential
warning markets might have no real intentions but filtersrsquo illusions
0 10 20 30 40 50 60-2
-1
0
1
2
3
4
011981 061985
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
- eg
Constructing Indicator-Oriented Strategieswith or without
Modeling
from empirical to theoretical
0 05 1 15 2 25 3 35 4-2
0
2
4
6
8
10H i+1
Si
Empirical Raw Optimal Strategy Theoretical Raw Optimal Strategy ΨΣ2
Methodological Framework of
Modeling Capital Markets
dynamics based on rationality oriented by memory filtered by dynamic kernel
Rational Memory Process
Ri+1-ri = Ψө(Di) + Ση(Di)middotεi+1
continuous-time approach (with a linear stationary filter)
dStSt = Ψө(int[0t]k(|τ-t|)middotSτ-1dSτ) middotdt + Ση(int[0t]k(|τ-t|)middotSτ
-1dSτ)middotdWt
Market Aggregation Rationality
Market Background Conditions
bull neatly constructing dynamic investment strategies on the dynamic domain
bull analytic calculation of risk-return trade-off curve via calculus of variation
bull easily formulating integrated-volatility for simulating risk-neutral probability density and calculating VaR
bull turning nonlinear dynamic auto-regression into static nonparametric regression
bull introducing adaptive statistical estimation methods to separate stationary and non-stationary factors
bull assessing modeling risk
bull paving a way to ldquostatistical financerdquo (market energy)
bull keeping the modeling framework flexible and adaptive under reflexivity
bull pricing profitable financial knowledges based on valuable dynamic kernels
Advantages on
Dynamic Domain
building robust amp adaptive models for financial engineering in magic domains
Multi-Resolutionof
Complex Market Time Series
wavelet-based decomposition to figure out market behavior features
1974 Great Stock Market Capitulation
1987 Great Stock Market Crash
1989 Nikkei Bubble Burst
1997 Asian Currency Crisis
1998 LTCM Fallout
2000 Nasdaq (Tech) Bubble Burst
Hard Lessons from
Markets
dynamic risks beyond interpretation of stochastic volatility (no anomaly talk)
Part IV
Rational Memory Processes
a canonical methodological frameworkof
capital market modeling based on
financial signal processing
bull Theoretical Issues (about mathematical analysis)bull Dynamics ndash Demand Supply Mechanism
bull Randomness ndash Uncertainty Structure (multi-scale noise structure)
bull Practical Issues (about paradigms)bull Market Sentiment ndash Momentum Uncertainty
bull Market Rationality ndash Prediction Risk-Return Trade-Off
bull Market Strategy ndash Arbitrage Risk Hedging Schemes
bull Market Efficiency amp Completeness ndash Financial Infrastructures Products
bull Market Liquidity amp Friction ndash Trading Volumes Cost Turn-Over rate
bull Market Constitution ndash Economical Cultural Geopolitical Backgrounds
bull Technical Issues (about applications and implications)bull Model Identification ndash Parameter Estimation
bull Model Assessment ndash Modeling Risk (Modeling Bias Estimation Loss)
bull Model Adaptation ndash Coefficient Relations to Econ and Other Marketsrsquo Conditions
bull Model Extensibility ndash Extension to Absorb New Factors counting for ldquoAnomaliesrdquo
Prospects for
Modeling Capital Markets
setting a modeling methodological framework to incorporate the prospects
Challenges for
Modeling Capital Markets
bull Non-linearity amp Non-stationarity in Signal Dynamics
bull Complexity in Signal Structure
bull Noise Barrier (Overwhelming Noise-to-Signal Ratio)
bull Nonparametric Estimation (MLE does not make sense anymore here)
Curse of Dimensionality
1 2 3 4 5 6 7 8 9 10 11 12
Piecewise (Monthly) Constant Geometric Brownian Motion
Ri = μ(Ri-1 Ri-2 hellip)+σ (Ri-1 Ri-2 hellip) εi
Technical Foundationfor
Financial Signal Processing
Transformation Magic to break Curse of Dimensionality
Analyzing Signals over Fourier Frequency Domain
Analyzing Signals in Wavelet Multi-Resolution Framework
Complexity in Signal Structure
Non-linearity amp Non-stationarity in Signal Dynamics
Analyzing Signals over Dynamic Domain
in
Wavelet Multi-Resolution Framework
Fundamental Signal Processing Tasksfor
Financial Engineering
an objective way to format market patterns from experience
FilterHistoric
Time SeriesTechnicalIndicator
DiS0 S1 hellip Si
Di =Г(S0 hellip Si V0 hellip Vi |өi)
Dt =Гt(Sτ[0t])continuous-time approach
special interested format
Di =Г(R1 hellip Ri) Rj = (Sj-Sj-1)Sj-1
linear stationary case
Di = c1middotR1 + hellip + cimiddotRi Dt = int[0t]k(|τ-t|)middotSτ-1dSτ
Examples of
Dynamic Indicators
Dancing with Cycles
0 100 200 300 400 500 600 700-5
-4
-3
-2
-1
0
1
2
3
4
5
121951 022003
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
Dynamic Indicators Technical Indicators which serve to monitor and gauge market cycles
Critical Patternsof
Long-Term Cyclic Phenomena
0 50 100 150-2
-1
0
1
2
3
4
Jul 1993
Oct 1987
Nov 1981
Feb 1986
MaxUncertaintyLine
12-Month STTB Moving Average 12-Month SampP500 Return MA ()
Principle of Cyclic Hazard
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
1285 1290 0496
0401
Nikkei 225 SampP 500
TAIEX
Example Iof
Short-Horizon Dynamic Patterns
catching rebounding points and finding implicit trend forces
Fidelity Emerging Markets Fund (USD)
Fidelity Technology Fund (EUR) Fidelity American Growth Fund (USD)
Fidelity World Fund (EUR)
08182003 0120204 08182003 0120204
08182003 0120204 08182003 0120204
Index Value
20-Day STTB
Example IIof
Short-Horizon Dynamic Patterns
catching a rebounding and surging point
20-Day STTB
Example IIIof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Currency Triangular Arbitraging
12-Month MA of USD-vs-EUR Return Rate
12-Month MA of USD-vs-JPY Return Rate
12-Month MA of USD-vs-EUR 12-M STTB
12-Month MA of USD-vs-JPY 12-M STTB
Example IVof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Stock-Index Triangular Arbitraging
02132003 01162004
TWSEBKITWSE Cumulative Relative Return Rate (3)
TWSEELECTWSE Cumulative Relative Return Rate (3)
5-Day MA of TWSEBKITWSE Relative 20-Day STTB
5-Day MA of TWSEELECTWSE Relative 20-Day STTB
bull Physical Meanings - indicating practical market sense eg momentum uncertainty stability liquidity hellip etc
bull Cycle-Leading
bull Consistency amp Universality (Time amp Geography)
Conditionsof
Modeling Potential
warning markets might have no real intentions but filtersrsquo illusions
0 10 20 30 40 50 60-2
-1
0
1
2
3
4
011981 061985
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
- eg
Constructing Indicator-Oriented Strategieswith or without
Modeling
from empirical to theoretical
0 05 1 15 2 25 3 35 4-2
0
2
4
6
8
10H i+1
Si
Empirical Raw Optimal Strategy Theoretical Raw Optimal Strategy ΨΣ2
Methodological Framework of
Modeling Capital Markets
dynamics based on rationality oriented by memory filtered by dynamic kernel
Rational Memory Process
Ri+1-ri = Ψө(Di) + Ση(Di)middotεi+1
continuous-time approach (with a linear stationary filter)
dStSt = Ψө(int[0t]k(|τ-t|)middotSτ-1dSτ) middotdt + Ση(int[0t]k(|τ-t|)middotSτ
-1dSτ)middotdWt
Market Aggregation Rationality
Market Background Conditions
bull neatly constructing dynamic investment strategies on the dynamic domain
bull analytic calculation of risk-return trade-off curve via calculus of variation
bull easily formulating integrated-volatility for simulating risk-neutral probability density and calculating VaR
bull turning nonlinear dynamic auto-regression into static nonparametric regression
bull introducing adaptive statistical estimation methods to separate stationary and non-stationary factors
bull assessing modeling risk
bull paving a way to ldquostatistical financerdquo (market energy)
bull keeping the modeling framework flexible and adaptive under reflexivity
bull pricing profitable financial knowledges based on valuable dynamic kernels
Advantages on
Dynamic Domain
building robust amp adaptive models for financial engineering in magic domains
1974 Great Stock Market Capitulation
1987 Great Stock Market Crash
1989 Nikkei Bubble Burst
1997 Asian Currency Crisis
1998 LTCM Fallout
2000 Nasdaq (Tech) Bubble Burst
Hard Lessons from
Markets
dynamic risks beyond interpretation of stochastic volatility (no anomaly talk)
Part IV
Rational Memory Processes
a canonical methodological frameworkof
capital market modeling based on
financial signal processing
bull Theoretical Issues (about mathematical analysis)bull Dynamics ndash Demand Supply Mechanism
bull Randomness ndash Uncertainty Structure (multi-scale noise structure)
bull Practical Issues (about paradigms)bull Market Sentiment ndash Momentum Uncertainty
bull Market Rationality ndash Prediction Risk-Return Trade-Off
bull Market Strategy ndash Arbitrage Risk Hedging Schemes
bull Market Efficiency amp Completeness ndash Financial Infrastructures Products
bull Market Liquidity amp Friction ndash Trading Volumes Cost Turn-Over rate
bull Market Constitution ndash Economical Cultural Geopolitical Backgrounds
bull Technical Issues (about applications and implications)bull Model Identification ndash Parameter Estimation
bull Model Assessment ndash Modeling Risk (Modeling Bias Estimation Loss)
bull Model Adaptation ndash Coefficient Relations to Econ and Other Marketsrsquo Conditions
bull Model Extensibility ndash Extension to Absorb New Factors counting for ldquoAnomaliesrdquo
Prospects for
Modeling Capital Markets
setting a modeling methodological framework to incorporate the prospects
Challenges for
Modeling Capital Markets
bull Non-linearity amp Non-stationarity in Signal Dynamics
bull Complexity in Signal Structure
bull Noise Barrier (Overwhelming Noise-to-Signal Ratio)
bull Nonparametric Estimation (MLE does not make sense anymore here)
Curse of Dimensionality
1 2 3 4 5 6 7 8 9 10 11 12
Piecewise (Monthly) Constant Geometric Brownian Motion
Ri = μ(Ri-1 Ri-2 hellip)+σ (Ri-1 Ri-2 hellip) εi
Technical Foundationfor
Financial Signal Processing
Transformation Magic to break Curse of Dimensionality
Analyzing Signals over Fourier Frequency Domain
Analyzing Signals in Wavelet Multi-Resolution Framework
Complexity in Signal Structure
Non-linearity amp Non-stationarity in Signal Dynamics
Analyzing Signals over Dynamic Domain
in
Wavelet Multi-Resolution Framework
Fundamental Signal Processing Tasksfor
Financial Engineering
an objective way to format market patterns from experience
FilterHistoric
Time SeriesTechnicalIndicator
DiS0 S1 hellip Si
Di =Г(S0 hellip Si V0 hellip Vi |өi)
Dt =Гt(Sτ[0t])continuous-time approach
special interested format
Di =Г(R1 hellip Ri) Rj = (Sj-Sj-1)Sj-1
linear stationary case
Di = c1middotR1 + hellip + cimiddotRi Dt = int[0t]k(|τ-t|)middotSτ-1dSτ
Examples of
Dynamic Indicators
Dancing with Cycles
0 100 200 300 400 500 600 700-5
-4
-3
-2
-1
0
1
2
3
4
5
121951 022003
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
Dynamic Indicators Technical Indicators which serve to monitor and gauge market cycles
Critical Patternsof
Long-Term Cyclic Phenomena
0 50 100 150-2
-1
0
1
2
3
4
Jul 1993
Oct 1987
Nov 1981
Feb 1986
MaxUncertaintyLine
12-Month STTB Moving Average 12-Month SampP500 Return MA ()
Principle of Cyclic Hazard
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
1285 1290 0496
0401
Nikkei 225 SampP 500
TAIEX
Example Iof
Short-Horizon Dynamic Patterns
catching rebounding points and finding implicit trend forces
Fidelity Emerging Markets Fund (USD)
Fidelity Technology Fund (EUR) Fidelity American Growth Fund (USD)
Fidelity World Fund (EUR)
08182003 0120204 08182003 0120204
08182003 0120204 08182003 0120204
Index Value
20-Day STTB
Example IIof
Short-Horizon Dynamic Patterns
catching a rebounding and surging point
20-Day STTB
Example IIIof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Currency Triangular Arbitraging
12-Month MA of USD-vs-EUR Return Rate
12-Month MA of USD-vs-JPY Return Rate
12-Month MA of USD-vs-EUR 12-M STTB
12-Month MA of USD-vs-JPY 12-M STTB
Example IVof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Stock-Index Triangular Arbitraging
02132003 01162004
TWSEBKITWSE Cumulative Relative Return Rate (3)
TWSEELECTWSE Cumulative Relative Return Rate (3)
5-Day MA of TWSEBKITWSE Relative 20-Day STTB
5-Day MA of TWSEELECTWSE Relative 20-Day STTB
bull Physical Meanings - indicating practical market sense eg momentum uncertainty stability liquidity hellip etc
bull Cycle-Leading
bull Consistency amp Universality (Time amp Geography)
Conditionsof
Modeling Potential
warning markets might have no real intentions but filtersrsquo illusions
0 10 20 30 40 50 60-2
-1
0
1
2
3
4
011981 061985
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
- eg
Constructing Indicator-Oriented Strategieswith or without
Modeling
from empirical to theoretical
0 05 1 15 2 25 3 35 4-2
0
2
4
6
8
10H i+1
Si
Empirical Raw Optimal Strategy Theoretical Raw Optimal Strategy ΨΣ2
Methodological Framework of
Modeling Capital Markets
dynamics based on rationality oriented by memory filtered by dynamic kernel
Rational Memory Process
Ri+1-ri = Ψө(Di) + Ση(Di)middotεi+1
continuous-time approach (with a linear stationary filter)
dStSt = Ψө(int[0t]k(|τ-t|)middotSτ-1dSτ) middotdt + Ση(int[0t]k(|τ-t|)middotSτ
-1dSτ)middotdWt
Market Aggregation Rationality
Market Background Conditions
bull neatly constructing dynamic investment strategies on the dynamic domain
bull analytic calculation of risk-return trade-off curve via calculus of variation
bull easily formulating integrated-volatility for simulating risk-neutral probability density and calculating VaR
bull turning nonlinear dynamic auto-regression into static nonparametric regression
bull introducing adaptive statistical estimation methods to separate stationary and non-stationary factors
bull assessing modeling risk
bull paving a way to ldquostatistical financerdquo (market energy)
bull keeping the modeling framework flexible and adaptive under reflexivity
bull pricing profitable financial knowledges based on valuable dynamic kernels
Advantages on
Dynamic Domain
building robust amp adaptive models for financial engineering in magic domains
Part IV
Rational Memory Processes
a canonical methodological frameworkof
capital market modeling based on
financial signal processing
bull Theoretical Issues (about mathematical analysis)bull Dynamics ndash Demand Supply Mechanism
bull Randomness ndash Uncertainty Structure (multi-scale noise structure)
bull Practical Issues (about paradigms)bull Market Sentiment ndash Momentum Uncertainty
bull Market Rationality ndash Prediction Risk-Return Trade-Off
bull Market Strategy ndash Arbitrage Risk Hedging Schemes
bull Market Efficiency amp Completeness ndash Financial Infrastructures Products
bull Market Liquidity amp Friction ndash Trading Volumes Cost Turn-Over rate
bull Market Constitution ndash Economical Cultural Geopolitical Backgrounds
bull Technical Issues (about applications and implications)bull Model Identification ndash Parameter Estimation
bull Model Assessment ndash Modeling Risk (Modeling Bias Estimation Loss)
bull Model Adaptation ndash Coefficient Relations to Econ and Other Marketsrsquo Conditions
bull Model Extensibility ndash Extension to Absorb New Factors counting for ldquoAnomaliesrdquo
Prospects for
Modeling Capital Markets
setting a modeling methodological framework to incorporate the prospects
Challenges for
Modeling Capital Markets
bull Non-linearity amp Non-stationarity in Signal Dynamics
bull Complexity in Signal Structure
bull Noise Barrier (Overwhelming Noise-to-Signal Ratio)
bull Nonparametric Estimation (MLE does not make sense anymore here)
Curse of Dimensionality
1 2 3 4 5 6 7 8 9 10 11 12
Piecewise (Monthly) Constant Geometric Brownian Motion
Ri = μ(Ri-1 Ri-2 hellip)+σ (Ri-1 Ri-2 hellip) εi
Technical Foundationfor
Financial Signal Processing
Transformation Magic to break Curse of Dimensionality
Analyzing Signals over Fourier Frequency Domain
Analyzing Signals in Wavelet Multi-Resolution Framework
Complexity in Signal Structure
Non-linearity amp Non-stationarity in Signal Dynamics
Analyzing Signals over Dynamic Domain
in
Wavelet Multi-Resolution Framework
Fundamental Signal Processing Tasksfor
Financial Engineering
an objective way to format market patterns from experience
FilterHistoric
Time SeriesTechnicalIndicator
DiS0 S1 hellip Si
Di =Г(S0 hellip Si V0 hellip Vi |өi)
Dt =Гt(Sτ[0t])continuous-time approach
special interested format
Di =Г(R1 hellip Ri) Rj = (Sj-Sj-1)Sj-1
linear stationary case
Di = c1middotR1 + hellip + cimiddotRi Dt = int[0t]k(|τ-t|)middotSτ-1dSτ
Examples of
Dynamic Indicators
Dancing with Cycles
0 100 200 300 400 500 600 700-5
-4
-3
-2
-1
0
1
2
3
4
5
121951 022003
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
Dynamic Indicators Technical Indicators which serve to monitor and gauge market cycles
Critical Patternsof
Long-Term Cyclic Phenomena
0 50 100 150-2
-1
0
1
2
3
4
Jul 1993
Oct 1987
Nov 1981
Feb 1986
MaxUncertaintyLine
12-Month STTB Moving Average 12-Month SampP500 Return MA ()
Principle of Cyclic Hazard
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
1285 1290 0496
0401
Nikkei 225 SampP 500
TAIEX
Example Iof
Short-Horizon Dynamic Patterns
catching rebounding points and finding implicit trend forces
Fidelity Emerging Markets Fund (USD)
Fidelity Technology Fund (EUR) Fidelity American Growth Fund (USD)
Fidelity World Fund (EUR)
08182003 0120204 08182003 0120204
08182003 0120204 08182003 0120204
Index Value
20-Day STTB
Example IIof
Short-Horizon Dynamic Patterns
catching a rebounding and surging point
20-Day STTB
Example IIIof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Currency Triangular Arbitraging
12-Month MA of USD-vs-EUR Return Rate
12-Month MA of USD-vs-JPY Return Rate
12-Month MA of USD-vs-EUR 12-M STTB
12-Month MA of USD-vs-JPY 12-M STTB
Example IVof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Stock-Index Triangular Arbitraging
02132003 01162004
TWSEBKITWSE Cumulative Relative Return Rate (3)
TWSEELECTWSE Cumulative Relative Return Rate (3)
5-Day MA of TWSEBKITWSE Relative 20-Day STTB
5-Day MA of TWSEELECTWSE Relative 20-Day STTB
bull Physical Meanings - indicating practical market sense eg momentum uncertainty stability liquidity hellip etc
bull Cycle-Leading
bull Consistency amp Universality (Time amp Geography)
Conditionsof
Modeling Potential
warning markets might have no real intentions but filtersrsquo illusions
0 10 20 30 40 50 60-2
-1
0
1
2
3
4
011981 061985
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
- eg
Constructing Indicator-Oriented Strategieswith or without
Modeling
from empirical to theoretical
0 05 1 15 2 25 3 35 4-2
0
2
4
6
8
10H i+1
Si
Empirical Raw Optimal Strategy Theoretical Raw Optimal Strategy ΨΣ2
Methodological Framework of
Modeling Capital Markets
dynamics based on rationality oriented by memory filtered by dynamic kernel
Rational Memory Process
Ri+1-ri = Ψө(Di) + Ση(Di)middotεi+1
continuous-time approach (with a linear stationary filter)
dStSt = Ψө(int[0t]k(|τ-t|)middotSτ-1dSτ) middotdt + Ση(int[0t]k(|τ-t|)middotSτ
-1dSτ)middotdWt
Market Aggregation Rationality
Market Background Conditions
bull neatly constructing dynamic investment strategies on the dynamic domain
bull analytic calculation of risk-return trade-off curve via calculus of variation
bull easily formulating integrated-volatility for simulating risk-neutral probability density and calculating VaR
bull turning nonlinear dynamic auto-regression into static nonparametric regression
bull introducing adaptive statistical estimation methods to separate stationary and non-stationary factors
bull assessing modeling risk
bull paving a way to ldquostatistical financerdquo (market energy)
bull keeping the modeling framework flexible and adaptive under reflexivity
bull pricing profitable financial knowledges based on valuable dynamic kernels
Advantages on
Dynamic Domain
building robust amp adaptive models for financial engineering in magic domains
bull Theoretical Issues (about mathematical analysis)bull Dynamics ndash Demand Supply Mechanism
bull Randomness ndash Uncertainty Structure (multi-scale noise structure)
bull Practical Issues (about paradigms)bull Market Sentiment ndash Momentum Uncertainty
bull Market Rationality ndash Prediction Risk-Return Trade-Off
bull Market Strategy ndash Arbitrage Risk Hedging Schemes
bull Market Efficiency amp Completeness ndash Financial Infrastructures Products
bull Market Liquidity amp Friction ndash Trading Volumes Cost Turn-Over rate
bull Market Constitution ndash Economical Cultural Geopolitical Backgrounds
bull Technical Issues (about applications and implications)bull Model Identification ndash Parameter Estimation
bull Model Assessment ndash Modeling Risk (Modeling Bias Estimation Loss)
bull Model Adaptation ndash Coefficient Relations to Econ and Other Marketsrsquo Conditions
bull Model Extensibility ndash Extension to Absorb New Factors counting for ldquoAnomaliesrdquo
Prospects for
Modeling Capital Markets
setting a modeling methodological framework to incorporate the prospects
Challenges for
Modeling Capital Markets
bull Non-linearity amp Non-stationarity in Signal Dynamics
bull Complexity in Signal Structure
bull Noise Barrier (Overwhelming Noise-to-Signal Ratio)
bull Nonparametric Estimation (MLE does not make sense anymore here)
Curse of Dimensionality
1 2 3 4 5 6 7 8 9 10 11 12
Piecewise (Monthly) Constant Geometric Brownian Motion
Ri = μ(Ri-1 Ri-2 hellip)+σ (Ri-1 Ri-2 hellip) εi
Technical Foundationfor
Financial Signal Processing
Transformation Magic to break Curse of Dimensionality
Analyzing Signals over Fourier Frequency Domain
Analyzing Signals in Wavelet Multi-Resolution Framework
Complexity in Signal Structure
Non-linearity amp Non-stationarity in Signal Dynamics
Analyzing Signals over Dynamic Domain
in
Wavelet Multi-Resolution Framework
Fundamental Signal Processing Tasksfor
Financial Engineering
an objective way to format market patterns from experience
FilterHistoric
Time SeriesTechnicalIndicator
DiS0 S1 hellip Si
Di =Г(S0 hellip Si V0 hellip Vi |өi)
Dt =Гt(Sτ[0t])continuous-time approach
special interested format
Di =Г(R1 hellip Ri) Rj = (Sj-Sj-1)Sj-1
linear stationary case
Di = c1middotR1 + hellip + cimiddotRi Dt = int[0t]k(|τ-t|)middotSτ-1dSτ
Examples of
Dynamic Indicators
Dancing with Cycles
0 100 200 300 400 500 600 700-5
-4
-3
-2
-1
0
1
2
3
4
5
121951 022003
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
Dynamic Indicators Technical Indicators which serve to monitor and gauge market cycles
Critical Patternsof
Long-Term Cyclic Phenomena
0 50 100 150-2
-1
0
1
2
3
4
Jul 1993
Oct 1987
Nov 1981
Feb 1986
MaxUncertaintyLine
12-Month STTB Moving Average 12-Month SampP500 Return MA ()
Principle of Cyclic Hazard
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
1285 1290 0496
0401
Nikkei 225 SampP 500
TAIEX
Example Iof
Short-Horizon Dynamic Patterns
catching rebounding points and finding implicit trend forces
Fidelity Emerging Markets Fund (USD)
Fidelity Technology Fund (EUR) Fidelity American Growth Fund (USD)
Fidelity World Fund (EUR)
08182003 0120204 08182003 0120204
08182003 0120204 08182003 0120204
Index Value
20-Day STTB
Example IIof
Short-Horizon Dynamic Patterns
catching a rebounding and surging point
20-Day STTB
Example IIIof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Currency Triangular Arbitraging
12-Month MA of USD-vs-EUR Return Rate
12-Month MA of USD-vs-JPY Return Rate
12-Month MA of USD-vs-EUR 12-M STTB
12-Month MA of USD-vs-JPY 12-M STTB
Example IVof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Stock-Index Triangular Arbitraging
02132003 01162004
TWSEBKITWSE Cumulative Relative Return Rate (3)
TWSEELECTWSE Cumulative Relative Return Rate (3)
5-Day MA of TWSEBKITWSE Relative 20-Day STTB
5-Day MA of TWSEELECTWSE Relative 20-Day STTB
bull Physical Meanings - indicating practical market sense eg momentum uncertainty stability liquidity hellip etc
bull Cycle-Leading
bull Consistency amp Universality (Time amp Geography)
Conditionsof
Modeling Potential
warning markets might have no real intentions but filtersrsquo illusions
0 10 20 30 40 50 60-2
-1
0
1
2
3
4
011981 061985
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
- eg
Constructing Indicator-Oriented Strategieswith or without
Modeling
from empirical to theoretical
0 05 1 15 2 25 3 35 4-2
0
2
4
6
8
10H i+1
Si
Empirical Raw Optimal Strategy Theoretical Raw Optimal Strategy ΨΣ2
Methodological Framework of
Modeling Capital Markets
dynamics based on rationality oriented by memory filtered by dynamic kernel
Rational Memory Process
Ri+1-ri = Ψө(Di) + Ση(Di)middotεi+1
continuous-time approach (with a linear stationary filter)
dStSt = Ψө(int[0t]k(|τ-t|)middotSτ-1dSτ) middotdt + Ση(int[0t]k(|τ-t|)middotSτ
-1dSτ)middotdWt
Market Aggregation Rationality
Market Background Conditions
bull neatly constructing dynamic investment strategies on the dynamic domain
bull analytic calculation of risk-return trade-off curve via calculus of variation
bull easily formulating integrated-volatility for simulating risk-neutral probability density and calculating VaR
bull turning nonlinear dynamic auto-regression into static nonparametric regression
bull introducing adaptive statistical estimation methods to separate stationary and non-stationary factors
bull assessing modeling risk
bull paving a way to ldquostatistical financerdquo (market energy)
bull keeping the modeling framework flexible and adaptive under reflexivity
bull pricing profitable financial knowledges based on valuable dynamic kernels
Advantages on
Dynamic Domain
building robust amp adaptive models for financial engineering in magic domains
Challenges for
Modeling Capital Markets
bull Non-linearity amp Non-stationarity in Signal Dynamics
bull Complexity in Signal Structure
bull Noise Barrier (Overwhelming Noise-to-Signal Ratio)
bull Nonparametric Estimation (MLE does not make sense anymore here)
Curse of Dimensionality
1 2 3 4 5 6 7 8 9 10 11 12
Piecewise (Monthly) Constant Geometric Brownian Motion
Ri = μ(Ri-1 Ri-2 hellip)+σ (Ri-1 Ri-2 hellip) εi
Technical Foundationfor
Financial Signal Processing
Transformation Magic to break Curse of Dimensionality
Analyzing Signals over Fourier Frequency Domain
Analyzing Signals in Wavelet Multi-Resolution Framework
Complexity in Signal Structure
Non-linearity amp Non-stationarity in Signal Dynamics
Analyzing Signals over Dynamic Domain
in
Wavelet Multi-Resolution Framework
Fundamental Signal Processing Tasksfor
Financial Engineering
an objective way to format market patterns from experience
FilterHistoric
Time SeriesTechnicalIndicator
DiS0 S1 hellip Si
Di =Г(S0 hellip Si V0 hellip Vi |өi)
Dt =Гt(Sτ[0t])continuous-time approach
special interested format
Di =Г(R1 hellip Ri) Rj = (Sj-Sj-1)Sj-1
linear stationary case
Di = c1middotR1 + hellip + cimiddotRi Dt = int[0t]k(|τ-t|)middotSτ-1dSτ
Examples of
Dynamic Indicators
Dancing with Cycles
0 100 200 300 400 500 600 700-5
-4
-3
-2
-1
0
1
2
3
4
5
121951 022003
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
Dynamic Indicators Technical Indicators which serve to monitor and gauge market cycles
Critical Patternsof
Long-Term Cyclic Phenomena
0 50 100 150-2
-1
0
1
2
3
4
Jul 1993
Oct 1987
Nov 1981
Feb 1986
MaxUncertaintyLine
12-Month STTB Moving Average 12-Month SampP500 Return MA ()
Principle of Cyclic Hazard
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
1285 1290 0496
0401
Nikkei 225 SampP 500
TAIEX
Example Iof
Short-Horizon Dynamic Patterns
catching rebounding points and finding implicit trend forces
Fidelity Emerging Markets Fund (USD)
Fidelity Technology Fund (EUR) Fidelity American Growth Fund (USD)
Fidelity World Fund (EUR)
08182003 0120204 08182003 0120204
08182003 0120204 08182003 0120204
Index Value
20-Day STTB
Example IIof
Short-Horizon Dynamic Patterns
catching a rebounding and surging point
20-Day STTB
Example IIIof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Currency Triangular Arbitraging
12-Month MA of USD-vs-EUR Return Rate
12-Month MA of USD-vs-JPY Return Rate
12-Month MA of USD-vs-EUR 12-M STTB
12-Month MA of USD-vs-JPY 12-M STTB
Example IVof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Stock-Index Triangular Arbitraging
02132003 01162004
TWSEBKITWSE Cumulative Relative Return Rate (3)
TWSEELECTWSE Cumulative Relative Return Rate (3)
5-Day MA of TWSEBKITWSE Relative 20-Day STTB
5-Day MA of TWSEELECTWSE Relative 20-Day STTB
bull Physical Meanings - indicating practical market sense eg momentum uncertainty stability liquidity hellip etc
bull Cycle-Leading
bull Consistency amp Universality (Time amp Geography)
Conditionsof
Modeling Potential
warning markets might have no real intentions but filtersrsquo illusions
0 10 20 30 40 50 60-2
-1
0
1
2
3
4
011981 061985
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
- eg
Constructing Indicator-Oriented Strategieswith or without
Modeling
from empirical to theoretical
0 05 1 15 2 25 3 35 4-2
0
2
4
6
8
10H i+1
Si
Empirical Raw Optimal Strategy Theoretical Raw Optimal Strategy ΨΣ2
Methodological Framework of
Modeling Capital Markets
dynamics based on rationality oriented by memory filtered by dynamic kernel
Rational Memory Process
Ri+1-ri = Ψө(Di) + Ση(Di)middotεi+1
continuous-time approach (with a linear stationary filter)
dStSt = Ψө(int[0t]k(|τ-t|)middotSτ-1dSτ) middotdt + Ση(int[0t]k(|τ-t|)middotSτ
-1dSτ)middotdWt
Market Aggregation Rationality
Market Background Conditions
bull neatly constructing dynamic investment strategies on the dynamic domain
bull analytic calculation of risk-return trade-off curve via calculus of variation
bull easily formulating integrated-volatility for simulating risk-neutral probability density and calculating VaR
bull turning nonlinear dynamic auto-regression into static nonparametric regression
bull introducing adaptive statistical estimation methods to separate stationary and non-stationary factors
bull assessing modeling risk
bull paving a way to ldquostatistical financerdquo (market energy)
bull keeping the modeling framework flexible and adaptive under reflexivity
bull pricing profitable financial knowledges based on valuable dynamic kernels
Advantages on
Dynamic Domain
building robust amp adaptive models for financial engineering in magic domains
Technical Foundationfor
Financial Signal Processing
Transformation Magic to break Curse of Dimensionality
Analyzing Signals over Fourier Frequency Domain
Analyzing Signals in Wavelet Multi-Resolution Framework
Complexity in Signal Structure
Non-linearity amp Non-stationarity in Signal Dynamics
Analyzing Signals over Dynamic Domain
in
Wavelet Multi-Resolution Framework
Fundamental Signal Processing Tasksfor
Financial Engineering
an objective way to format market patterns from experience
FilterHistoric
Time SeriesTechnicalIndicator
DiS0 S1 hellip Si
Di =Г(S0 hellip Si V0 hellip Vi |өi)
Dt =Гt(Sτ[0t])continuous-time approach
special interested format
Di =Г(R1 hellip Ri) Rj = (Sj-Sj-1)Sj-1
linear stationary case
Di = c1middotR1 + hellip + cimiddotRi Dt = int[0t]k(|τ-t|)middotSτ-1dSτ
Examples of
Dynamic Indicators
Dancing with Cycles
0 100 200 300 400 500 600 700-5
-4
-3
-2
-1
0
1
2
3
4
5
121951 022003
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
Dynamic Indicators Technical Indicators which serve to monitor and gauge market cycles
Critical Patternsof
Long-Term Cyclic Phenomena
0 50 100 150-2
-1
0
1
2
3
4
Jul 1993
Oct 1987
Nov 1981
Feb 1986
MaxUncertaintyLine
12-Month STTB Moving Average 12-Month SampP500 Return MA ()
Principle of Cyclic Hazard
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
1285 1290 0496
0401
Nikkei 225 SampP 500
TAIEX
Example Iof
Short-Horizon Dynamic Patterns
catching rebounding points and finding implicit trend forces
Fidelity Emerging Markets Fund (USD)
Fidelity Technology Fund (EUR) Fidelity American Growth Fund (USD)
Fidelity World Fund (EUR)
08182003 0120204 08182003 0120204
08182003 0120204 08182003 0120204
Index Value
20-Day STTB
Example IIof
Short-Horizon Dynamic Patterns
catching a rebounding and surging point
20-Day STTB
Example IIIof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Currency Triangular Arbitraging
12-Month MA of USD-vs-EUR Return Rate
12-Month MA of USD-vs-JPY Return Rate
12-Month MA of USD-vs-EUR 12-M STTB
12-Month MA of USD-vs-JPY 12-M STTB
Example IVof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Stock-Index Triangular Arbitraging
02132003 01162004
TWSEBKITWSE Cumulative Relative Return Rate (3)
TWSEELECTWSE Cumulative Relative Return Rate (3)
5-Day MA of TWSEBKITWSE Relative 20-Day STTB
5-Day MA of TWSEELECTWSE Relative 20-Day STTB
bull Physical Meanings - indicating practical market sense eg momentum uncertainty stability liquidity hellip etc
bull Cycle-Leading
bull Consistency amp Universality (Time amp Geography)
Conditionsof
Modeling Potential
warning markets might have no real intentions but filtersrsquo illusions
0 10 20 30 40 50 60-2
-1
0
1
2
3
4
011981 061985
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
- eg
Constructing Indicator-Oriented Strategieswith or without
Modeling
from empirical to theoretical
0 05 1 15 2 25 3 35 4-2
0
2
4
6
8
10H i+1
Si
Empirical Raw Optimal Strategy Theoretical Raw Optimal Strategy ΨΣ2
Methodological Framework of
Modeling Capital Markets
dynamics based on rationality oriented by memory filtered by dynamic kernel
Rational Memory Process
Ri+1-ri = Ψө(Di) + Ση(Di)middotεi+1
continuous-time approach (with a linear stationary filter)
dStSt = Ψө(int[0t]k(|τ-t|)middotSτ-1dSτ) middotdt + Ση(int[0t]k(|τ-t|)middotSτ
-1dSτ)middotdWt
Market Aggregation Rationality
Market Background Conditions
bull neatly constructing dynamic investment strategies on the dynamic domain
bull analytic calculation of risk-return trade-off curve via calculus of variation
bull easily formulating integrated-volatility for simulating risk-neutral probability density and calculating VaR
bull turning nonlinear dynamic auto-regression into static nonparametric regression
bull introducing adaptive statistical estimation methods to separate stationary and non-stationary factors
bull assessing modeling risk
bull paving a way to ldquostatistical financerdquo (market energy)
bull keeping the modeling framework flexible and adaptive under reflexivity
bull pricing profitable financial knowledges based on valuable dynamic kernels
Advantages on
Dynamic Domain
building robust amp adaptive models for financial engineering in magic domains
Fundamental Signal Processing Tasksfor
Financial Engineering
an objective way to format market patterns from experience
FilterHistoric
Time SeriesTechnicalIndicator
DiS0 S1 hellip Si
Di =Г(S0 hellip Si V0 hellip Vi |өi)
Dt =Гt(Sτ[0t])continuous-time approach
special interested format
Di =Г(R1 hellip Ri) Rj = (Sj-Sj-1)Sj-1
linear stationary case
Di = c1middotR1 + hellip + cimiddotRi Dt = int[0t]k(|τ-t|)middotSτ-1dSτ
Examples of
Dynamic Indicators
Dancing with Cycles
0 100 200 300 400 500 600 700-5
-4
-3
-2
-1
0
1
2
3
4
5
121951 022003
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
Dynamic Indicators Technical Indicators which serve to monitor and gauge market cycles
Critical Patternsof
Long-Term Cyclic Phenomena
0 50 100 150-2
-1
0
1
2
3
4
Jul 1993
Oct 1987
Nov 1981
Feb 1986
MaxUncertaintyLine
12-Month STTB Moving Average 12-Month SampP500 Return MA ()
Principle of Cyclic Hazard
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
1285 1290 0496
0401
Nikkei 225 SampP 500
TAIEX
Example Iof
Short-Horizon Dynamic Patterns
catching rebounding points and finding implicit trend forces
Fidelity Emerging Markets Fund (USD)
Fidelity Technology Fund (EUR) Fidelity American Growth Fund (USD)
Fidelity World Fund (EUR)
08182003 0120204 08182003 0120204
08182003 0120204 08182003 0120204
Index Value
20-Day STTB
Example IIof
Short-Horizon Dynamic Patterns
catching a rebounding and surging point
20-Day STTB
Example IIIof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Currency Triangular Arbitraging
12-Month MA of USD-vs-EUR Return Rate
12-Month MA of USD-vs-JPY Return Rate
12-Month MA of USD-vs-EUR 12-M STTB
12-Month MA of USD-vs-JPY 12-M STTB
Example IVof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Stock-Index Triangular Arbitraging
02132003 01162004
TWSEBKITWSE Cumulative Relative Return Rate (3)
TWSEELECTWSE Cumulative Relative Return Rate (3)
5-Day MA of TWSEBKITWSE Relative 20-Day STTB
5-Day MA of TWSEELECTWSE Relative 20-Day STTB
bull Physical Meanings - indicating practical market sense eg momentum uncertainty stability liquidity hellip etc
bull Cycle-Leading
bull Consistency amp Universality (Time amp Geography)
Conditionsof
Modeling Potential
warning markets might have no real intentions but filtersrsquo illusions
0 10 20 30 40 50 60-2
-1
0
1
2
3
4
011981 061985
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
- eg
Constructing Indicator-Oriented Strategieswith or without
Modeling
from empirical to theoretical
0 05 1 15 2 25 3 35 4-2
0
2
4
6
8
10H i+1
Si
Empirical Raw Optimal Strategy Theoretical Raw Optimal Strategy ΨΣ2
Methodological Framework of
Modeling Capital Markets
dynamics based on rationality oriented by memory filtered by dynamic kernel
Rational Memory Process
Ri+1-ri = Ψө(Di) + Ση(Di)middotεi+1
continuous-time approach (with a linear stationary filter)
dStSt = Ψө(int[0t]k(|τ-t|)middotSτ-1dSτ) middotdt + Ση(int[0t]k(|τ-t|)middotSτ
-1dSτ)middotdWt
Market Aggregation Rationality
Market Background Conditions
bull neatly constructing dynamic investment strategies on the dynamic domain
bull analytic calculation of risk-return trade-off curve via calculus of variation
bull easily formulating integrated-volatility for simulating risk-neutral probability density and calculating VaR
bull turning nonlinear dynamic auto-regression into static nonparametric regression
bull introducing adaptive statistical estimation methods to separate stationary and non-stationary factors
bull assessing modeling risk
bull paving a way to ldquostatistical financerdquo (market energy)
bull keeping the modeling framework flexible and adaptive under reflexivity
bull pricing profitable financial knowledges based on valuable dynamic kernels
Advantages on
Dynamic Domain
building robust amp adaptive models for financial engineering in magic domains
Examples of
Dynamic Indicators
Dancing with Cycles
0 100 200 300 400 500 600 700-5
-4
-3
-2
-1
0
1
2
3
4
5
121951 022003
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
Dynamic Indicators Technical Indicators which serve to monitor and gauge market cycles
Critical Patternsof
Long-Term Cyclic Phenomena
0 50 100 150-2
-1
0
1
2
3
4
Jul 1993
Oct 1987
Nov 1981
Feb 1986
MaxUncertaintyLine
12-Month STTB Moving Average 12-Month SampP500 Return MA ()
Principle of Cyclic Hazard
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
1285 1290 0496
0401
Nikkei 225 SampP 500
TAIEX
Example Iof
Short-Horizon Dynamic Patterns
catching rebounding points and finding implicit trend forces
Fidelity Emerging Markets Fund (USD)
Fidelity Technology Fund (EUR) Fidelity American Growth Fund (USD)
Fidelity World Fund (EUR)
08182003 0120204 08182003 0120204
08182003 0120204 08182003 0120204
Index Value
20-Day STTB
Example IIof
Short-Horizon Dynamic Patterns
catching a rebounding and surging point
20-Day STTB
Example IIIof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Currency Triangular Arbitraging
12-Month MA of USD-vs-EUR Return Rate
12-Month MA of USD-vs-JPY Return Rate
12-Month MA of USD-vs-EUR 12-M STTB
12-Month MA of USD-vs-JPY 12-M STTB
Example IVof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Stock-Index Triangular Arbitraging
02132003 01162004
TWSEBKITWSE Cumulative Relative Return Rate (3)
TWSEELECTWSE Cumulative Relative Return Rate (3)
5-Day MA of TWSEBKITWSE Relative 20-Day STTB
5-Day MA of TWSEELECTWSE Relative 20-Day STTB
bull Physical Meanings - indicating practical market sense eg momentum uncertainty stability liquidity hellip etc
bull Cycle-Leading
bull Consistency amp Universality (Time amp Geography)
Conditionsof
Modeling Potential
warning markets might have no real intentions but filtersrsquo illusions
0 10 20 30 40 50 60-2
-1
0
1
2
3
4
011981 061985
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
- eg
Constructing Indicator-Oriented Strategieswith or without
Modeling
from empirical to theoretical
0 05 1 15 2 25 3 35 4-2
0
2
4
6
8
10H i+1
Si
Empirical Raw Optimal Strategy Theoretical Raw Optimal Strategy ΨΣ2
Methodological Framework of
Modeling Capital Markets
dynamics based on rationality oriented by memory filtered by dynamic kernel
Rational Memory Process
Ri+1-ri = Ψө(Di) + Ση(Di)middotεi+1
continuous-time approach (with a linear stationary filter)
dStSt = Ψө(int[0t]k(|τ-t|)middotSτ-1dSτ) middotdt + Ση(int[0t]k(|τ-t|)middotSτ
-1dSτ)middotdWt
Market Aggregation Rationality
Market Background Conditions
bull neatly constructing dynamic investment strategies on the dynamic domain
bull analytic calculation of risk-return trade-off curve via calculus of variation
bull easily formulating integrated-volatility for simulating risk-neutral probability density and calculating VaR
bull turning nonlinear dynamic auto-regression into static nonparametric regression
bull introducing adaptive statistical estimation methods to separate stationary and non-stationary factors
bull assessing modeling risk
bull paving a way to ldquostatistical financerdquo (market energy)
bull keeping the modeling framework flexible and adaptive under reflexivity
bull pricing profitable financial knowledges based on valuable dynamic kernels
Advantages on
Dynamic Domain
building robust amp adaptive models for financial engineering in magic domains
Critical Patternsof
Long-Term Cyclic Phenomena
0 50 100 150-2
-1
0
1
2
3
4
Jul 1993
Oct 1987
Nov 1981
Feb 1986
MaxUncertaintyLine
12-Month STTB Moving Average 12-Month SampP500 Return MA ()
Principle of Cyclic Hazard
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
0 20 40 60-4
-3
-2
-1
0
1
2
3
4
1285 1290 0496
0401
Nikkei 225 SampP 500
TAIEX
Example Iof
Short-Horizon Dynamic Patterns
catching rebounding points and finding implicit trend forces
Fidelity Emerging Markets Fund (USD)
Fidelity Technology Fund (EUR) Fidelity American Growth Fund (USD)
Fidelity World Fund (EUR)
08182003 0120204 08182003 0120204
08182003 0120204 08182003 0120204
Index Value
20-Day STTB
Example IIof
Short-Horizon Dynamic Patterns
catching a rebounding and surging point
20-Day STTB
Example IIIof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Currency Triangular Arbitraging
12-Month MA of USD-vs-EUR Return Rate
12-Month MA of USD-vs-JPY Return Rate
12-Month MA of USD-vs-EUR 12-M STTB
12-Month MA of USD-vs-JPY 12-M STTB
Example IVof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Stock-Index Triangular Arbitraging
02132003 01162004
TWSEBKITWSE Cumulative Relative Return Rate (3)
TWSEELECTWSE Cumulative Relative Return Rate (3)
5-Day MA of TWSEBKITWSE Relative 20-Day STTB
5-Day MA of TWSEELECTWSE Relative 20-Day STTB
bull Physical Meanings - indicating practical market sense eg momentum uncertainty stability liquidity hellip etc
bull Cycle-Leading
bull Consistency amp Universality (Time amp Geography)
Conditionsof
Modeling Potential
warning markets might have no real intentions but filtersrsquo illusions
0 10 20 30 40 50 60-2
-1
0
1
2
3
4
011981 061985
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
- eg
Constructing Indicator-Oriented Strategieswith or without
Modeling
from empirical to theoretical
0 05 1 15 2 25 3 35 4-2
0
2
4
6
8
10H i+1
Si
Empirical Raw Optimal Strategy Theoretical Raw Optimal Strategy ΨΣ2
Methodological Framework of
Modeling Capital Markets
dynamics based on rationality oriented by memory filtered by dynamic kernel
Rational Memory Process
Ri+1-ri = Ψө(Di) + Ση(Di)middotεi+1
continuous-time approach (with a linear stationary filter)
dStSt = Ψө(int[0t]k(|τ-t|)middotSτ-1dSτ) middotdt + Ση(int[0t]k(|τ-t|)middotSτ
-1dSτ)middotdWt
Market Aggregation Rationality
Market Background Conditions
bull neatly constructing dynamic investment strategies on the dynamic domain
bull analytic calculation of risk-return trade-off curve via calculus of variation
bull easily formulating integrated-volatility for simulating risk-neutral probability density and calculating VaR
bull turning nonlinear dynamic auto-regression into static nonparametric regression
bull introducing adaptive statistical estimation methods to separate stationary and non-stationary factors
bull assessing modeling risk
bull paving a way to ldquostatistical financerdquo (market energy)
bull keeping the modeling framework flexible and adaptive under reflexivity
bull pricing profitable financial knowledges based on valuable dynamic kernels
Advantages on
Dynamic Domain
building robust amp adaptive models for financial engineering in magic domains
Example Iof
Short-Horizon Dynamic Patterns
catching rebounding points and finding implicit trend forces
Fidelity Emerging Markets Fund (USD)
Fidelity Technology Fund (EUR) Fidelity American Growth Fund (USD)
Fidelity World Fund (EUR)
08182003 0120204 08182003 0120204
08182003 0120204 08182003 0120204
Index Value
20-Day STTB
Example IIof
Short-Horizon Dynamic Patterns
catching a rebounding and surging point
20-Day STTB
Example IIIof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Currency Triangular Arbitraging
12-Month MA of USD-vs-EUR Return Rate
12-Month MA of USD-vs-JPY Return Rate
12-Month MA of USD-vs-EUR 12-M STTB
12-Month MA of USD-vs-JPY 12-M STTB
Example IVof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Stock-Index Triangular Arbitraging
02132003 01162004
TWSEBKITWSE Cumulative Relative Return Rate (3)
TWSEELECTWSE Cumulative Relative Return Rate (3)
5-Day MA of TWSEBKITWSE Relative 20-Day STTB
5-Day MA of TWSEELECTWSE Relative 20-Day STTB
bull Physical Meanings - indicating practical market sense eg momentum uncertainty stability liquidity hellip etc
bull Cycle-Leading
bull Consistency amp Universality (Time amp Geography)
Conditionsof
Modeling Potential
warning markets might have no real intentions but filtersrsquo illusions
0 10 20 30 40 50 60-2
-1
0
1
2
3
4
011981 061985
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
- eg
Constructing Indicator-Oriented Strategieswith or without
Modeling
from empirical to theoretical
0 05 1 15 2 25 3 35 4-2
0
2
4
6
8
10H i+1
Si
Empirical Raw Optimal Strategy Theoretical Raw Optimal Strategy ΨΣ2
Methodological Framework of
Modeling Capital Markets
dynamics based on rationality oriented by memory filtered by dynamic kernel
Rational Memory Process
Ri+1-ri = Ψө(Di) + Ση(Di)middotεi+1
continuous-time approach (with a linear stationary filter)
dStSt = Ψө(int[0t]k(|τ-t|)middotSτ-1dSτ) middotdt + Ση(int[0t]k(|τ-t|)middotSτ
-1dSτ)middotdWt
Market Aggregation Rationality
Market Background Conditions
bull neatly constructing dynamic investment strategies on the dynamic domain
bull analytic calculation of risk-return trade-off curve via calculus of variation
bull easily formulating integrated-volatility for simulating risk-neutral probability density and calculating VaR
bull turning nonlinear dynamic auto-regression into static nonparametric regression
bull introducing adaptive statistical estimation methods to separate stationary and non-stationary factors
bull assessing modeling risk
bull paving a way to ldquostatistical financerdquo (market energy)
bull keeping the modeling framework flexible and adaptive under reflexivity
bull pricing profitable financial knowledges based on valuable dynamic kernels
Advantages on
Dynamic Domain
building robust amp adaptive models for financial engineering in magic domains
Example IIof
Short-Horizon Dynamic Patterns
catching a rebounding and surging point
20-Day STTB
Example IIIof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Currency Triangular Arbitraging
12-Month MA of USD-vs-EUR Return Rate
12-Month MA of USD-vs-JPY Return Rate
12-Month MA of USD-vs-EUR 12-M STTB
12-Month MA of USD-vs-JPY 12-M STTB
Example IVof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Stock-Index Triangular Arbitraging
02132003 01162004
TWSEBKITWSE Cumulative Relative Return Rate (3)
TWSEELECTWSE Cumulative Relative Return Rate (3)
5-Day MA of TWSEBKITWSE Relative 20-Day STTB
5-Day MA of TWSEELECTWSE Relative 20-Day STTB
bull Physical Meanings - indicating practical market sense eg momentum uncertainty stability liquidity hellip etc
bull Cycle-Leading
bull Consistency amp Universality (Time amp Geography)
Conditionsof
Modeling Potential
warning markets might have no real intentions but filtersrsquo illusions
0 10 20 30 40 50 60-2
-1
0
1
2
3
4
011981 061985
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
- eg
Constructing Indicator-Oriented Strategieswith or without
Modeling
from empirical to theoretical
0 05 1 15 2 25 3 35 4-2
0
2
4
6
8
10H i+1
Si
Empirical Raw Optimal Strategy Theoretical Raw Optimal Strategy ΨΣ2
Methodological Framework of
Modeling Capital Markets
dynamics based on rationality oriented by memory filtered by dynamic kernel
Rational Memory Process
Ri+1-ri = Ψө(Di) + Ση(Di)middotεi+1
continuous-time approach (with a linear stationary filter)
dStSt = Ψө(int[0t]k(|τ-t|)middotSτ-1dSτ) middotdt + Ση(int[0t]k(|τ-t|)middotSτ
-1dSτ)middotdWt
Market Aggregation Rationality
Market Background Conditions
bull neatly constructing dynamic investment strategies on the dynamic domain
bull analytic calculation of risk-return trade-off curve via calculus of variation
bull easily formulating integrated-volatility for simulating risk-neutral probability density and calculating VaR
bull turning nonlinear dynamic auto-regression into static nonparametric regression
bull introducing adaptive statistical estimation methods to separate stationary and non-stationary factors
bull assessing modeling risk
bull paving a way to ldquostatistical financerdquo (market energy)
bull keeping the modeling framework flexible and adaptive under reflexivity
bull pricing profitable financial knowledges based on valuable dynamic kernels
Advantages on
Dynamic Domain
building robust amp adaptive models for financial engineering in magic domains
Example IIIof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Currency Triangular Arbitraging
12-Month MA of USD-vs-EUR Return Rate
12-Month MA of USD-vs-JPY Return Rate
12-Month MA of USD-vs-EUR 12-M STTB
12-Month MA of USD-vs-JPY 12-M STTB
Example IVof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Stock-Index Triangular Arbitraging
02132003 01162004
TWSEBKITWSE Cumulative Relative Return Rate (3)
TWSEELECTWSE Cumulative Relative Return Rate (3)
5-Day MA of TWSEBKITWSE Relative 20-Day STTB
5-Day MA of TWSEELECTWSE Relative 20-Day STTB
bull Physical Meanings - indicating practical market sense eg momentum uncertainty stability liquidity hellip etc
bull Cycle-Leading
bull Consistency amp Universality (Time amp Geography)
Conditionsof
Modeling Potential
warning markets might have no real intentions but filtersrsquo illusions
0 10 20 30 40 50 60-2
-1
0
1
2
3
4
011981 061985
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
- eg
Constructing Indicator-Oriented Strategieswith or without
Modeling
from empirical to theoretical
0 05 1 15 2 25 3 35 4-2
0
2
4
6
8
10H i+1
Si
Empirical Raw Optimal Strategy Theoretical Raw Optimal Strategy ΨΣ2
Methodological Framework of
Modeling Capital Markets
dynamics based on rationality oriented by memory filtered by dynamic kernel
Rational Memory Process
Ri+1-ri = Ψө(Di) + Ση(Di)middotεi+1
continuous-time approach (with a linear stationary filter)
dStSt = Ψө(int[0t]k(|τ-t|)middotSτ-1dSτ) middotdt + Ση(int[0t]k(|τ-t|)middotSτ
-1dSτ)middotdWt
Market Aggregation Rationality
Market Background Conditions
bull neatly constructing dynamic investment strategies on the dynamic domain
bull analytic calculation of risk-return trade-off curve via calculus of variation
bull easily formulating integrated-volatility for simulating risk-neutral probability density and calculating VaR
bull turning nonlinear dynamic auto-regression into static nonparametric regression
bull introducing adaptive statistical estimation methods to separate stationary and non-stationary factors
bull assessing modeling risk
bull paving a way to ldquostatistical financerdquo (market energy)
bull keeping the modeling framework flexible and adaptive under reflexivity
bull pricing profitable financial knowledges based on valuable dynamic kernels
Advantages on
Dynamic Domain
building robust amp adaptive models for financial engineering in magic domains
Example IVof
Short-Horizon Dynamic Patterns
Helicoid Pattern of Stock-Index Triangular Arbitraging
02132003 01162004
TWSEBKITWSE Cumulative Relative Return Rate (3)
TWSEELECTWSE Cumulative Relative Return Rate (3)
5-Day MA of TWSEBKITWSE Relative 20-Day STTB
5-Day MA of TWSEELECTWSE Relative 20-Day STTB
bull Physical Meanings - indicating practical market sense eg momentum uncertainty stability liquidity hellip etc
bull Cycle-Leading
bull Consistency amp Universality (Time amp Geography)
Conditionsof
Modeling Potential
warning markets might have no real intentions but filtersrsquo illusions
0 10 20 30 40 50 60-2
-1
0
1
2
3
4
011981 061985
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
- eg
Constructing Indicator-Oriented Strategieswith or without
Modeling
from empirical to theoretical
0 05 1 15 2 25 3 35 4-2
0
2
4
6
8
10H i+1
Si
Empirical Raw Optimal Strategy Theoretical Raw Optimal Strategy ΨΣ2
Methodological Framework of
Modeling Capital Markets
dynamics based on rationality oriented by memory filtered by dynamic kernel
Rational Memory Process
Ri+1-ri = Ψө(Di) + Ση(Di)middotεi+1
continuous-time approach (with a linear stationary filter)
dStSt = Ψө(int[0t]k(|τ-t|)middotSτ-1dSτ) middotdt + Ση(int[0t]k(|τ-t|)middotSτ
-1dSτ)middotdWt
Market Aggregation Rationality
Market Background Conditions
bull neatly constructing dynamic investment strategies on the dynamic domain
bull analytic calculation of risk-return trade-off curve via calculus of variation
bull easily formulating integrated-volatility for simulating risk-neutral probability density and calculating VaR
bull turning nonlinear dynamic auto-regression into static nonparametric regression
bull introducing adaptive statistical estimation methods to separate stationary and non-stationary factors
bull assessing modeling risk
bull paving a way to ldquostatistical financerdquo (market energy)
bull keeping the modeling framework flexible and adaptive under reflexivity
bull pricing profitable financial knowledges based on valuable dynamic kernels
Advantages on
Dynamic Domain
building robust amp adaptive models for financial engineering in magic domains
bull Physical Meanings - indicating practical market sense eg momentum uncertainty stability liquidity hellip etc
bull Cycle-Leading
bull Consistency amp Universality (Time amp Geography)
Conditionsof
Modeling Potential
warning markets might have no real intentions but filtersrsquo illusions
0 10 20 30 40 50 60-2
-1
0
1
2
3
4
011981 061985
Monthly STTB
12-Month STTB Moving Average
12-Month SampP 500 Return Rate M A ()
- eg
Constructing Indicator-Oriented Strategieswith or without
Modeling
from empirical to theoretical
0 05 1 15 2 25 3 35 4-2
0
2
4
6
8
10H i+1
Si
Empirical Raw Optimal Strategy Theoretical Raw Optimal Strategy ΨΣ2
Methodological Framework of
Modeling Capital Markets
dynamics based on rationality oriented by memory filtered by dynamic kernel
Rational Memory Process
Ri+1-ri = Ψө(Di) + Ση(Di)middotεi+1
continuous-time approach (with a linear stationary filter)
dStSt = Ψө(int[0t]k(|τ-t|)middotSτ-1dSτ) middotdt + Ση(int[0t]k(|τ-t|)middotSτ
-1dSτ)middotdWt
Market Aggregation Rationality
Market Background Conditions
bull neatly constructing dynamic investment strategies on the dynamic domain
bull analytic calculation of risk-return trade-off curve via calculus of variation
bull easily formulating integrated-volatility for simulating risk-neutral probability density and calculating VaR
bull turning nonlinear dynamic auto-regression into static nonparametric regression
bull introducing adaptive statistical estimation methods to separate stationary and non-stationary factors
bull assessing modeling risk
bull paving a way to ldquostatistical financerdquo (market energy)
bull keeping the modeling framework flexible and adaptive under reflexivity
bull pricing profitable financial knowledges based on valuable dynamic kernels
Advantages on
Dynamic Domain
building robust amp adaptive models for financial engineering in magic domains
Constructing Indicator-Oriented Strategieswith or without
Modeling
from empirical to theoretical
0 05 1 15 2 25 3 35 4-2
0
2
4
6
8
10H i+1
Si
Empirical Raw Optimal Strategy Theoretical Raw Optimal Strategy ΨΣ2
Methodological Framework of
Modeling Capital Markets
dynamics based on rationality oriented by memory filtered by dynamic kernel
Rational Memory Process
Ri+1-ri = Ψө(Di) + Ση(Di)middotεi+1
continuous-time approach (with a linear stationary filter)
dStSt = Ψө(int[0t]k(|τ-t|)middotSτ-1dSτ) middotdt + Ση(int[0t]k(|τ-t|)middotSτ
-1dSτ)middotdWt
Market Aggregation Rationality
Market Background Conditions
bull neatly constructing dynamic investment strategies on the dynamic domain
bull analytic calculation of risk-return trade-off curve via calculus of variation
bull easily formulating integrated-volatility for simulating risk-neutral probability density and calculating VaR
bull turning nonlinear dynamic auto-regression into static nonparametric regression
bull introducing adaptive statistical estimation methods to separate stationary and non-stationary factors
bull assessing modeling risk
bull paving a way to ldquostatistical financerdquo (market energy)
bull keeping the modeling framework flexible and adaptive under reflexivity
bull pricing profitable financial knowledges based on valuable dynamic kernels
Advantages on
Dynamic Domain
building robust amp adaptive models for financial engineering in magic domains
Methodological Framework of
Modeling Capital Markets
dynamics based on rationality oriented by memory filtered by dynamic kernel
Rational Memory Process
Ri+1-ri = Ψө(Di) + Ση(Di)middotεi+1
continuous-time approach (with a linear stationary filter)
dStSt = Ψө(int[0t]k(|τ-t|)middotSτ-1dSτ) middotdt + Ση(int[0t]k(|τ-t|)middotSτ
-1dSτ)middotdWt
Market Aggregation Rationality
Market Background Conditions
bull neatly constructing dynamic investment strategies on the dynamic domain
bull analytic calculation of risk-return trade-off curve via calculus of variation
bull easily formulating integrated-volatility for simulating risk-neutral probability density and calculating VaR
bull turning nonlinear dynamic auto-regression into static nonparametric regression
bull introducing adaptive statistical estimation methods to separate stationary and non-stationary factors
bull assessing modeling risk
bull paving a way to ldquostatistical financerdquo (market energy)
bull keeping the modeling framework flexible and adaptive under reflexivity
bull pricing profitable financial knowledges based on valuable dynamic kernels
Advantages on
Dynamic Domain
building robust amp adaptive models for financial engineering in magic domains
bull neatly constructing dynamic investment strategies on the dynamic domain
bull analytic calculation of risk-return trade-off curve via calculus of variation
bull easily formulating integrated-volatility for simulating risk-neutral probability density and calculating VaR
bull turning nonlinear dynamic auto-regression into static nonparametric regression
bull introducing adaptive statistical estimation methods to separate stationary and non-stationary factors
bull assessing modeling risk
bull paving a way to ldquostatistical financerdquo (market energy)
bull keeping the modeling framework flexible and adaptive under reflexivity
bull pricing profitable financial knowledges based on valuable dynamic kernels
Advantages on
Dynamic Domain
building robust amp adaptive models for financial engineering in magic domains
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