Modeling Capital Markets with Financial Signal processing Bridging Technical Analysis &...

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


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


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



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


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


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


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


catching a rebounding and surging point

20-Day STTB

Example IIIof


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


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



- 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


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

Modeling Capital Markets with Financial Signal processing

Slide 2

Capturing Movements of Capital Markets

Dynamic Analysis of Market Movements

Slide 5

Reading Charts of Market Movements

Finding Technical Patterns of Market Demand-Supply

Technical Analysis as Financial Signal Processing

Strength and Weakness of Technical Analysis

Slide 10

Slide 11

Academic Canonical Frameworks of Capital Market Modeling

Finding Clues for Verifying Models

Strength and Weakness of Stochastic-Process Modeling

Slide 15

The Complex Reality for Thoughts

Multi-Resolution of Complex Market Time Series

Hard Lessons from Markets

Slide 19

Prospects for Modeling Capital Markets

Challenges for Modeling Capital Markets

Technical Foundation for Financial Signal Processing

Fundamental Signal Processing Tasks for Financial Engineering

Examples of Dynamic Indicators

Critical Patterns of Long-Term Cyclic Phenomena

Example I of Short-Horizon Dynamic Patterns

Example II of Short-Horizon Dynamic Patterns

Example III of Short-Horizon Dynamic Patterns

Example IV of Short-Horizon Dynamic Patterns

Conditions of Modeling Potential

Constructing Indicator-Oriented Strategies with or without Modeling

Methodological Framework of Modeling Capital Markets

Advantages on Dynamic Domain

a step toward

Rational Memory ProcessCanonical Foundation of Financial Engineering by Sifeon


Capital Markets




Dynamic Analysis of

Market Movements





Endogenous








Part I

Elementary Ideas in

Technical Analysis


Reading Charts of

Market Movements



Uncertainty

Momentum









Strategy



creating cycles




eg







Technical Analysis


Part II








Ri = (Si-Si-1)Si-1







(Auto-Regression)







σi 2 = α0+Σp

j=1αj εi-j2 +Σq

j=1βj σ i-j2






Finding Clues for

Verifying Models
















Part III

Reality amp

Lessons






bull Reflexivity


Thoughts


can

deal with it

GARCH

Multi-Resolutionof







1998 LTCM Fallout


Hard Lessons from

Markets


Part IV

















Prospects for



Challenges for







1 2 3 4 5 6 7 8 9 10 11 12











in





FilterHistoric


DiS0 S1 hellip Si







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




Critical Patternsof


0 50 100 150-2

-1

0

1

2

3

4

Jul 1993

Oct 1987

Nov 1981

Feb 1986

MaxUncertaintyLine



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


TAIEX

Example Iof






08182003 0120204 08182003 0120204

08182003 0120204 08182003 0120204

Index Value

20-Day STTB

Example IIof



20-Day STTB

Example IIIof







Example IVof



02132003 01162004






bull Cycle-Leading


Conditionsof

Modeling Potential


0 10 20 30 40 50 60-2

-1

0

1

2

3

4

011981 061985

Monthly STTB



- eg


Modeling


0 05 1 15 2 25 3 35 4-2

0

2

4

6

8

10H i+1

Si









-1dSτ)middotdWt












Advantages on

Dynamic Domain



Slide 2



Slide 5





Slide 10

Slide 11




Slide 15




Slide 19
















Capital Markets




Dynamic Analysis of

Market Movements





Endogenous








Part I

Elementary Ideas in

Technical Analysis


Reading Charts of

Market Movements



Uncertainty

Momentum









Strategy



creating cycles




eg







Technical Analysis


Part II








Ri = (Si-Si-1)Si-1







(Auto-Regression)







σi 2 = α0+Σp

j=1αj εi-j2 +Σq

j=1βj σ i-j2






Finding Clues for

Verifying Models
















Part III

Reality amp

Lessons






bull Reflexivity


Thoughts


can

deal with it

GARCH

Multi-Resolutionof







1998 LTCM Fallout


Hard Lessons from

Markets


Part IV

















Prospects for



Challenges for







1 2 3 4 5 6 7 8 9 10 11 12











in





FilterHistoric


DiS0 S1 hellip Si







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




Critical Patternsof


0 50 100 150-2

-1

0

1

2

3

4

Jul 1993

Oct 1987

Nov 1981

Feb 1986

MaxUncertaintyLine



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


TAIEX

Example Iof






08182003 0120204 08182003 0120204

08182003 0120204 08182003 0120204

Index Value

20-Day STTB

Example IIof



20-Day STTB

Example IIIof







Example IVof



02132003 01162004






bull Cycle-Leading


Conditionsof

Modeling Potential


0 10 20 30 40 50 60-2

-1

0

1

2

3

4

011981 061985

Monthly STTB



- eg


Modeling


0 05 1 15 2 25 3 35 4-2

0

2

4

6

8

10H i+1

Si









-1dSτ)middotdWt












Advantages on

Dynamic Domain



Slide 2



Slide 5





Slide 10

Slide 11




Slide 15




Slide 19















Dynamic Analysis of

Market Movements





Endogenous








Part I

Elementary Ideas in

Technical Analysis


Reading Charts of

Market Movements



Uncertainty

Momentum









Strategy



creating cycles




eg







Technical Analysis


Part II








Ri = (Si-Si-1)Si-1







(Auto-Regression)







σi 2 = α0+Σp

j=1αj εi-j2 +Σq

j=1βj σ i-j2






Finding Clues for

Verifying Models
















Part III

Reality amp

Lessons






bull Reflexivity


Thoughts


can

deal with it

GARCH

Multi-Resolutionof







1998 LTCM Fallout


Hard Lessons from

Markets


Part IV

















Prospects for



Challenges for







1 2 3 4 5 6 7 8 9 10 11 12











in





FilterHistoric


DiS0 S1 hellip Si







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




Critical Patternsof


0 50 100 150-2

-1

0

1

2

3

4

Jul 1993

Oct 1987

Nov 1981

Feb 1986

MaxUncertaintyLine



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


TAIEX

Example Iof






08182003 0120204 08182003 0120204

08182003 0120204 08182003 0120204

Index Value

20-Day STTB

Example IIof



20-Day STTB

Example IIIof







Example IVof



02132003 01162004






bull Cycle-Leading


Conditionsof

Modeling Potential


0 10 20 30 40 50 60-2

-1

0

1

2

3

4

011981 061985

Monthly STTB



- eg


Modeling


0 05 1 15 2 25 3 35 4-2

0

2

4

6

8

10H i+1

Si









-1dSτ)middotdWt












Advantages on

Dynamic Domain



Slide 2



Slide 5





Slide 10

Slide 11




Slide 15




Slide 19















Part I

Elementary Ideas in

Technical Analysis


Reading Charts of

Market Movements



Uncertainty

Momentum









Strategy



creating cycles




eg







Technical Analysis


Part II








Ri = (Si-Si-1)Si-1







(Auto-Regression)







σi 2 = α0+Σp

j=1αj εi-j2 +Σq

j=1βj σ i-j2






Finding Clues for

Verifying Models
















Part III

Reality amp

Lessons






bull Reflexivity


Thoughts


can

deal with it

GARCH

Multi-Resolutionof







1998 LTCM Fallout


Hard Lessons from

Markets


Part IV

















Prospects for



Challenges for







1 2 3 4 5 6 7 8 9 10 11 12











in





FilterHistoric


DiS0 S1 hellip Si







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




Critical Patternsof


0 50 100 150-2

-1

0

1

2

3

4

Jul 1993

Oct 1987

Nov 1981

Feb 1986

MaxUncertaintyLine



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


TAIEX

Example Iof






08182003 0120204 08182003 0120204

08182003 0120204 08182003 0120204

Index Value

20-Day STTB

Example IIof



20-Day STTB

Example IIIof







Example IVof



02132003 01162004






bull Cycle-Leading


Conditionsof

Modeling Potential


0 10 20 30 40 50 60-2

-1

0

1

2

3

4

011981 061985

Monthly STTB



- eg


Modeling


0 05 1 15 2 25 3 35 4-2

0

2

4

6

8

10H i+1

Si









-1dSτ)middotdWt












Advantages on

Dynamic Domain



Slide 2



Slide 5





Slide 10

Slide 11




Slide 15




Slide 19















Reading Charts of

Market Movements



Uncertainty

Momentum









Strategy



creating cycles




eg







Technical Analysis


Part II








Ri = (Si-Si-1)Si-1







(Auto-Regression)







σi 2 = α0+Σp

j=1αj εi-j2 +Σq

j=1βj σ i-j2






Finding Clues for

Verifying Models
















Part III

Reality amp

Lessons






bull Reflexivity


Thoughts


can

deal with it

GARCH

Multi-Resolutionof







1998 LTCM Fallout


Hard Lessons from

Markets


Part IV

















Prospects for



Challenges for







1 2 3 4 5 6 7 8 9 10 11 12











in





FilterHistoric


DiS0 S1 hellip Si







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




Critical Patternsof


0 50 100 150-2

-1

0

1

2

3

4

Jul 1993

Oct 1987

Nov 1981

Feb 1986

MaxUncertaintyLine



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


TAIEX

Example Iof






08182003 0120204 08182003 0120204

08182003 0120204 08182003 0120204

Index Value

20-Day STTB

Example IIof



20-Day STTB

Example IIIof







Example IVof



02132003 01162004






bull Cycle-Leading


Conditionsof

Modeling Potential


0 10 20 30 40 50 60-2

-1

0

1

2

3

4

011981 061985

Monthly STTB



- eg


Modeling


0 05 1 15 2 25 3 35 4-2

0

2

4

6

8

10H i+1

Si









-1dSτ)middotdWt












Advantages on

Dynamic Domain



Slide 2



Slide 5





Slide 10

Slide 11




Slide 15




Slide 19























Strategy



creating cycles




eg







Technical Analysis


Part II








Ri = (Si-Si-1)Si-1







(Auto-Regression)







σi 2 = α0+Σp

j=1αj εi-j2 +Σq

j=1βj σ i-j2






Finding Clues for

Verifying Models
















Part III

Reality amp

Lessons






bull Reflexivity


Thoughts


can

deal with it

GARCH

Multi-Resolutionof







1998 LTCM Fallout


Hard Lessons from

Markets


Part IV

















Prospects for



Challenges for







1 2 3 4 5 6 7 8 9 10 11 12











in





FilterHistoric


DiS0 S1 hellip Si







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




Critical Patternsof


0 50 100 150-2

-1

0

1

2

3

4

Jul 1993

Oct 1987

Nov 1981

Feb 1986

MaxUncertaintyLine



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


TAIEX

Example Iof






08182003 0120204 08182003 0120204

08182003 0120204 08182003 0120204

Index Value

20-Day STTB

Example IIof



20-Day STTB

Example IIIof







Example IVof



02132003 01162004






bull Cycle-Leading


Conditionsof

Modeling Potential


0 10 20 30 40 50 60-2

-1

0

1

2

3

4

011981 061985

Monthly STTB



- eg


Modeling


0 05 1 15 2 25 3 35 4-2

0

2

4

6

8

10H i+1

Si









-1dSτ)middotdWt












Advantages on

Dynamic Domain



Slide 2



Slide 5





Slide 10

Slide 11




Slide 15




Slide 19


















eg







Technical Analysis


Part II








Ri = (Si-Si-1)Si-1







(Auto-Regression)







σi 2 = α0+Σp

j=1αj εi-j2 +Σq

j=1βj σ i-j2






Finding Clues for

Verifying Models
















Part III

Reality amp

Lessons






bull Reflexivity


Thoughts


can

deal with it

GARCH

Multi-Resolutionof







1998 LTCM Fallout


Hard Lessons from

Markets


Part IV

















Prospects for



Challenges for







1 2 3 4 5 6 7 8 9 10 11 12











in





FilterHistoric


DiS0 S1 hellip Si







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




Critical Patternsof


0 50 100 150-2

-1

0

1

2

3

4

Jul 1993

Oct 1987

Nov 1981

Feb 1986

MaxUncertaintyLine



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


TAIEX

Example Iof






08182003 0120204 08182003 0120204

08182003 0120204 08182003 0120204

Index Value

20-Day STTB

Example IIof



20-Day STTB

Example IIIof







Example IVof



02132003 01162004






bull Cycle-Leading


Conditionsof

Modeling Potential


0 10 20 30 40 50 60-2

-1

0

1

2

3

4

011981 061985

Monthly STTB



- eg


Modeling


0 05 1 15 2 25 3 35 4-2

0

2

4

6

8

10H i+1

Si









-1dSτ)middotdWt












Advantages on

Dynamic Domain



Slide 2



Slide 5





Slide 10

Slide 11




Slide 15




Slide 19















Part II








Ri = (Si-Si-1)Si-1







(Auto-Regression)







σi 2 = α0+Σp

j=1αj εi-j2 +Σq

j=1βj σ i-j2






Finding Clues for

Verifying Models
















Part III

Reality amp

Lessons






bull Reflexivity


Thoughts


can

deal with it

GARCH

Multi-Resolutionof







1998 LTCM Fallout


Hard Lessons from

Markets


Part IV

















Prospects for



Challenges for







1 2 3 4 5 6 7 8 9 10 11 12











in





FilterHistoric


DiS0 S1 hellip Si







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




Critical Patternsof


0 50 100 150-2

-1

0

1

2

3

4

Jul 1993

Oct 1987

Nov 1981

Feb 1986

MaxUncertaintyLine



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


TAIEX

Example Iof






08182003 0120204 08182003 0120204

08182003 0120204 08182003 0120204

Index Value

20-Day STTB

Example IIof



20-Day STTB

Example IIIof







Example IVof



02132003 01162004






bull Cycle-Leading


Conditionsof

Modeling Potential


0 10 20 30 40 50 60-2

-1

0

1

2

3

4

011981 061985

Monthly STTB



- eg


Modeling


0 05 1 15 2 25 3 35 4-2

0

2

4

6

8

10H i+1

Si









-1dSτ)middotdWt












Advantages on

Dynamic Domain



Slide 2



Slide 5





Slide 10

Slide 11




Slide 15




Slide 19



















Ri = (Si-Si-1)Si-1







(Auto-Regression)







σi 2 = α0+Σp

j=1αj εi-j2 +Σq

j=1βj σ i-j2






Finding Clues for

Verifying Models
















Part III

Reality amp

Lessons






bull Reflexivity


Thoughts


can

deal with it

GARCH

Multi-Resolutionof







1998 LTCM Fallout


Hard Lessons from

Markets


Part IV

















Prospects for



Challenges for







1 2 3 4 5 6 7 8 9 10 11 12











in





FilterHistoric


DiS0 S1 hellip Si







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




Critical Patternsof


0 50 100 150-2

-1

0

1

2

3

4

Jul 1993

Oct 1987

Nov 1981

Feb 1986

MaxUncertaintyLine



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


TAIEX

Example Iof






08182003 0120204 08182003 0120204

08182003 0120204 08182003 0120204

Index Value

20-Day STTB

Example IIof



20-Day STTB

Example IIIof







Example IVof



02132003 01162004






bull Cycle-Leading


Conditionsof

Modeling Potential


0 10 20 30 40 50 60-2

-1

0

1

2

3

4

011981 061985

Monthly STTB



- eg


Modeling


0 05 1 15 2 25 3 35 4-2

0

2

4

6

8

10H i+1

Si









-1dSτ)middotdWt












Advantages on

Dynamic Domain



Slide 2



Slide 5





Slide 10

Slide 11




Slide 15




Slide 19


















(Auto-Regression)







σi 2 = α0+Σp

j=1αj εi-j2 +Σq

j=1βj σ i-j2






Finding Clues for

Verifying Models
















Part III

Reality amp

Lessons






bull Reflexivity


Thoughts


can

deal with it

GARCH

Multi-Resolutionof







1998 LTCM Fallout


Hard Lessons from

Markets


Part IV

















Prospects for



Challenges for







1 2 3 4 5 6 7 8 9 10 11 12











in





FilterHistoric


DiS0 S1 hellip Si







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




Critical Patternsof


0 50 100 150-2

-1

0

1

2

3

4

Jul 1993

Oct 1987

Nov 1981

Feb 1986

MaxUncertaintyLine



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


TAIEX

Example Iof






08182003 0120204 08182003 0120204

08182003 0120204 08182003 0120204

Index Value

20-Day STTB

Example IIof



20-Day STTB

Example IIIof







Example IVof



02132003 01162004






bull Cycle-Leading


Conditionsof

Modeling Potential


0 10 20 30 40 50 60-2

-1

0

1

2

3

4

011981 061985

Monthly STTB



- eg


Modeling


0 05 1 15 2 25 3 35 4-2

0

2

4

6

8

10H i+1

Si









-1dSτ)middotdWt












Advantages on

Dynamic Domain



Slide 2



Slide 5





Slide 10

Slide 11




Slide 15




Slide 19















Finding Clues for

Verifying Models
















Part III

Reality amp

Lessons






bull Reflexivity


Thoughts


can

deal with it

GARCH

Multi-Resolutionof







1998 LTCM Fallout


Hard Lessons from

Markets


Part IV

















Prospects for



Challenges for







1 2 3 4 5 6 7 8 9 10 11 12











in





FilterHistoric


DiS0 S1 hellip Si







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




Critical Patternsof


0 50 100 150-2

-1

0

1

2

3

4

Jul 1993

Oct 1987

Nov 1981

Feb 1986

MaxUncertaintyLine



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


TAIEX

Example Iof






08182003 0120204 08182003 0120204

08182003 0120204 08182003 0120204

Index Value

20-Day STTB

Example IIof



20-Day STTB

Example IIIof







Example IVof



02132003 01162004






bull Cycle-Leading


Conditionsof

Modeling Potential


0 10 20 30 40 50 60-2

-1

0

1

2

3

4

011981 061985

Monthly STTB



- eg


Modeling


0 05 1 15 2 25 3 35 4-2

0

2

4

6

8

10H i+1

Si









-1dSτ)middotdWt












Advantages on

Dynamic Domain



Slide 2



Slide 5





Slide 10

Slide 11




Slide 15




Slide 19


























Part III

Reality amp

Lessons






bull Reflexivity


Thoughts


can

deal with it

GARCH

Multi-Resolutionof







1998 LTCM Fallout


Hard Lessons from

Markets


Part IV

















Prospects for



Challenges for







1 2 3 4 5 6 7 8 9 10 11 12











in





FilterHistoric


DiS0 S1 hellip Si







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




Critical Patternsof


0 50 100 150-2

-1

0

1

2

3

4

Jul 1993

Oct 1987

Nov 1981

Feb 1986

MaxUncertaintyLine



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


TAIEX

Example Iof






08182003 0120204 08182003 0120204

08182003 0120204 08182003 0120204

Index Value

20-Day STTB

Example IIof



20-Day STTB

Example IIIof







Example IVof



02132003 01162004






bull Cycle-Leading


Conditionsof

Modeling Potential


0 10 20 30 40 50 60-2

-1

0

1

2

3

4

011981 061985

Monthly STTB



- eg


Modeling


0 05 1 15 2 25 3 35 4-2

0

2

4

6

8

10H i+1

Si









-1dSτ)middotdWt












Advantages on

Dynamic Domain



Slide 2



Slide 5





Slide 10

Slide 11




Slide 15




Slide 19



















bull Reflexivity


Thoughts


can

deal with it

GARCH

Multi-Resolutionof







1998 LTCM Fallout


Hard Lessons from

Markets


Part IV

















Prospects for



Challenges for







1 2 3 4 5 6 7 8 9 10 11 12











in





FilterHistoric


DiS0 S1 hellip Si







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




Critical Patternsof


0 50 100 150-2

-1

0

1

2

3

4

Jul 1993

Oct 1987

Nov 1981

Feb 1986

MaxUncertaintyLine



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


TAIEX

Example Iof






08182003 0120204 08182003 0120204

08182003 0120204 08182003 0120204

Index Value

20-Day STTB

Example IIof



20-Day STTB

Example IIIof







Example IVof



02132003 01162004






bull Cycle-Leading


Conditionsof

Modeling Potential


0 10 20 30 40 50 60-2

-1

0

1

2

3

4

011981 061985

Monthly STTB



- eg


Modeling


0 05 1 15 2 25 3 35 4-2

0

2

4

6

8

10H i+1

Si









-1dSτ)middotdWt












Advantages on

Dynamic Domain



Slide 2



Slide 5





Slide 10

Slide 11




Slide 15




Slide 19















Multi-Resolutionof







1998 LTCM Fallout


Hard Lessons from

Markets


Part IV

















Prospects for



Challenges for







1 2 3 4 5 6 7 8 9 10 11 12











in





FilterHistoric


DiS0 S1 hellip Si







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




Critical Patternsof


0 50 100 150-2

-1

0

1

2

3

4

Jul 1993

Oct 1987

Nov 1981

Feb 1986

MaxUncertaintyLine



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


TAIEX

Example Iof






08182003 0120204 08182003 0120204

08182003 0120204 08182003 0120204

Index Value

20-Day STTB

Example IIof



20-Day STTB

Example IIIof







Example IVof



02132003 01162004






bull Cycle-Leading


Conditionsof

Modeling Potential


0 10 20 30 40 50 60-2

-1

0

1

2

3

4

011981 061985

Monthly STTB



- eg


Modeling


0 05 1 15 2 25 3 35 4-2

0

2

4

6

8

10H i+1

Si









-1dSτ)middotdWt












Advantages on

Dynamic Domain



Slide 2



Slide 5





Slide 10

Slide 11




Slide 15




Slide 19



















1998 LTCM Fallout


Hard Lessons from

Markets


Part IV

















Prospects for



Challenges for







1 2 3 4 5 6 7 8 9 10 11 12











in





FilterHistoric


DiS0 S1 hellip Si







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




Critical Patternsof


0 50 100 150-2

-1

0

1

2

3

4

Jul 1993

Oct 1987

Nov 1981

Feb 1986

MaxUncertaintyLine



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


TAIEX

Example Iof






08182003 0120204 08182003 0120204

08182003 0120204 08182003 0120204

Index Value

20-Day STTB

Example IIof



20-Day STTB

Example IIIof







Example IVof



02132003 01162004






bull Cycle-Leading


Conditionsof

Modeling Potential


0 10 20 30 40 50 60-2

-1

0

1

2

3

4

011981 061985

Monthly STTB



- eg


Modeling


0 05 1 15 2 25 3 35 4-2

0

2

4

6

8

10H i+1

Si









-1dSτ)middotdWt












Advantages on

Dynamic Domain



Slide 2



Slide 5





Slide 10

Slide 11




Slide 15




Slide 19















Part IV

















Prospects for



Challenges for







1 2 3 4 5 6 7 8 9 10 11 12











in





FilterHistoric


DiS0 S1 hellip Si







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




Critical Patternsof


0 50 100 150-2

-1

0

1

2

3

4

Jul 1993

Oct 1987

Nov 1981

Feb 1986

MaxUncertaintyLine



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


TAIEX

Example Iof






08182003 0120204 08182003 0120204

08182003 0120204 08182003 0120204

Index Value

20-Day STTB

Example IIof



20-Day STTB

Example IIIof







Example IVof



02132003 01162004






bull Cycle-Leading


Conditionsof

Modeling Potential


0 10 20 30 40 50 60-2

-1

0

1

2

3

4

011981 061985

Monthly STTB



- eg


Modeling


0 05 1 15 2 25 3 35 4-2

0

2

4

6

8

10H i+1

Si









-1dSτ)middotdWt












Advantages on

Dynamic Domain



Slide 2



Slide 5





Slide 10

Slide 11




Slide 15




Slide 19



























Prospects for



Challenges for







1 2 3 4 5 6 7 8 9 10 11 12











in





FilterHistoric


DiS0 S1 hellip Si







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




Critical Patternsof


0 50 100 150-2

-1

0

1

2

3

4

Jul 1993

Oct 1987

Nov 1981

Feb 1986

MaxUncertaintyLine



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


TAIEX

Example Iof






08182003 0120204 08182003 0120204

08182003 0120204 08182003 0120204

Index Value

20-Day STTB

Example IIof



20-Day STTB

Example IIIof







Example IVof



02132003 01162004






bull Cycle-Leading


Conditionsof

Modeling Potential


0 10 20 30 40 50 60-2

-1

0

1

2

3

4

011981 061985

Monthly STTB



- eg


Modeling


0 05 1 15 2 25 3 35 4-2

0

2

4

6

8

10H i+1

Si









-1dSτ)middotdWt












Advantages on

Dynamic Domain



Slide 2



Slide 5





Slide 10

Slide 11




Slide 15




Slide 19















Challenges for







1 2 3 4 5 6 7 8 9 10 11 12











in





FilterHistoric


DiS0 S1 hellip Si







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




Critical Patternsof


0 50 100 150-2

-1

0

1

2

3

4

Jul 1993

Oct 1987

Nov 1981

Feb 1986

MaxUncertaintyLine



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


TAIEX

Example Iof






08182003 0120204 08182003 0120204

08182003 0120204 08182003 0120204

Index Value

20-Day STTB

Example IIof



20-Day STTB

Example IIIof







Example IVof



02132003 01162004






bull Cycle-Leading


Conditionsof

Modeling Potential


0 10 20 30 40 50 60-2

-1

0

1

2

3

4

011981 061985

Monthly STTB



- eg


Modeling


0 05 1 15 2 25 3 35 4-2

0

2

4

6

8

10H i+1

Si









-1dSτ)middotdWt












Advantages on

Dynamic Domain



Slide 2



Slide 5





Slide 10

Slide 11




Slide 15




Slide 19























in





FilterHistoric


DiS0 S1 hellip Si







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




Critical Patternsof


0 50 100 150-2

-1

0

1

2

3

4

Jul 1993

Oct 1987

Nov 1981

Feb 1986

MaxUncertaintyLine



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


TAIEX

Example Iof






08182003 0120204 08182003 0120204

08182003 0120204 08182003 0120204

Index Value

20-Day STTB

Example IIof



20-Day STTB

Example IIIof







Example IVof



02132003 01162004






bull Cycle-Leading


Conditionsof

Modeling Potential


0 10 20 30 40 50 60-2

-1

0

1

2

3

4

011981 061985

Monthly STTB



- eg


Modeling


0 05 1 15 2 25 3 35 4-2

0

2

4

6

8

10H i+1

Si









-1dSτ)middotdWt












Advantages on

Dynamic Domain



Slide 2



Slide 5





Slide 10

Slide 11




Slide 15




Slide 19


















FilterHistoric


DiS0 S1 hellip Si







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




Critical Patternsof


0 50 100 150-2

-1

0

1

2

3

4

Jul 1993

Oct 1987

Nov 1981

Feb 1986

MaxUncertaintyLine



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


TAIEX

Example Iof






08182003 0120204 08182003 0120204

08182003 0120204 08182003 0120204

Index Value

20-Day STTB

Example IIof



20-Day STTB

Example IIIof







Example IVof



02132003 01162004






bull Cycle-Leading


Conditionsof

Modeling Potential


0 10 20 30 40 50 60-2

-1

0

1

2

3

4

011981 061985

Monthly STTB



- eg


Modeling


0 05 1 15 2 25 3 35 4-2

0

2

4

6

8

10H i+1

Si









-1dSτ)middotdWt












Advantages on

Dynamic Domain



Slide 2



Slide 5





Slide 10

Slide 11




Slide 15




Slide 19















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




Critical Patternsof


0 50 100 150-2

-1

0

1

2

3

4

Jul 1993

Oct 1987

Nov 1981

Feb 1986

MaxUncertaintyLine



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


TAIEX

Example Iof






08182003 0120204 08182003 0120204

08182003 0120204 08182003 0120204

Index Value

20-Day STTB

Example IIof



20-Day STTB

Example IIIof







Example IVof



02132003 01162004






bull Cycle-Leading


Conditionsof

Modeling Potential


0 10 20 30 40 50 60-2

-1

0

1

2

3

4

011981 061985

Monthly STTB



- eg


Modeling


0 05 1 15 2 25 3 35 4-2

0

2

4

6

8

10H i+1

Si









-1dSτ)middotdWt












Advantages on

Dynamic Domain



Slide 2



Slide 5





Slide 10

Slide 11




Slide 15




Slide 19















Critical Patternsof


0 50 100 150-2

-1

0

1

2

3

4

Jul 1993

Oct 1987

Nov 1981

Feb 1986

MaxUncertaintyLine



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


TAIEX

Example Iof






08182003 0120204 08182003 0120204

08182003 0120204 08182003 0120204

Index Value

20-Day STTB

Example IIof



20-Day STTB

Example IIIof







Example IVof



02132003 01162004






bull Cycle-Leading


Conditionsof

Modeling Potential


0 10 20 30 40 50 60-2

-1

0

1

2

3

4

011981 061985

Monthly STTB



- eg


Modeling


0 05 1 15 2 25 3 35 4-2

0

2

4

6

8

10H i+1

Si









-1dSτ)middotdWt












Advantages on

Dynamic Domain



Slide 2



Slide 5





Slide 10

Slide 11




Slide 15




Slide 19















Example Iof






08182003 0120204 08182003 0120204

08182003 0120204 08182003 0120204

Index Value

20-Day STTB

Example IIof



20-Day STTB

Example IIIof







Example IVof



02132003 01162004






bull Cycle-Leading


Conditionsof

Modeling Potential


0 10 20 30 40 50 60-2

-1

0

1

2

3

4

011981 061985

Monthly STTB



- eg


Modeling


0 05 1 15 2 25 3 35 4-2

0

2

4

6

8

10H i+1

Si









-1dSτ)middotdWt












Advantages on

Dynamic Domain



Slide 2



Slide 5





Slide 10

Slide 11




Slide 15




Slide 19















Example IIof



20-Day STTB

Example IIIof







Example IVof



02132003 01162004






bull Cycle-Leading


Conditionsof

Modeling Potential


0 10 20 30 40 50 60-2

-1

0

1

2

3

4

011981 061985

Monthly STTB



- eg


Modeling


0 05 1 15 2 25 3 35 4-2

0

2

4

6

8

10H i+1

Si









-1dSτ)middotdWt












Advantages on

Dynamic Domain



Slide 2



Slide 5





Slide 10

Slide 11




Slide 15




Slide 19















Example IIIof







Example IVof



02132003 01162004






bull Cycle-Leading


Conditionsof

Modeling Potential


0 10 20 30 40 50 60-2

-1

0

1

2

3

4

011981 061985

Monthly STTB



- eg


Modeling


0 05 1 15 2 25 3 35 4-2

0

2

4

6

8

10H i+1

Si









-1dSτ)middotdWt












Advantages on

Dynamic Domain



Slide 2



Slide 5





Slide 10

Slide 11




Slide 15




Slide 19















Example IVof



02132003 01162004






bull Cycle-Leading


Conditionsof

Modeling Potential


0 10 20 30 40 50 60-2

-1

0

1

2

3

4

011981 061985

Monthly STTB



- eg


Modeling


0 05 1 15 2 25 3 35 4-2

0

2

4

6

8

10H i+1

Si









-1dSτ)middotdWt












Advantages on

Dynamic Domain



Slide 2



Slide 5





Slide 10

Slide 11




Slide 15




Slide 19
















bull Cycle-Leading


Conditionsof

Modeling Potential


0 10 20 30 40 50 60-2

-1

0

1

2

3

4

011981 061985

Monthly STTB



- eg


Modeling


0 05 1 15 2 25 3 35 4-2

0

2

4

6

8

10H i+1

Si









-1dSτ)middotdWt












Advantages on

Dynamic Domain



Slide 2



Slide 5





Slide 10

Slide 11




Slide 15




Slide 19
















Modeling


0 05 1 15 2 25 3 35 4-2

0

2

4

6

8

10H i+1

Si









-1dSτ)middotdWt












Advantages on

Dynamic Domain



Slide 2



Slide 5





Slide 10

Slide 11




Slide 15




Slide 19






















-1dSτ)middotdWt












Advantages on

Dynamic Domain



Slide 2



Slide 5





Slide 10

Slide 11




Slide 15




Slide 19
























Advantages on

Dynamic Domain



Slide 2



Slide 5





Slide 10

Slide 11




Slide 15




Slide 19















Modeling Capital Markets with Financial Signal processing Bridging Technical Analysis &...

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Transcript of Modeling Capital Markets with Financial Signal processing Bridging Technical Analysis &...