FORECASTING THE RETURN OF BITCOIN EXCHANGE RATE

LYDIA NJERI NDUTA-SC283-2872/2011SUZZY BUTEMBU LAVENTA-SC283-

2915/2011SUPERVISOR: DR. A. WAITITU

INTRODUCTION

Bitcoin is an online form of digital currency developed by Sakoshi Nakamoto.

Transactions work across peer-to-peer network.

It is not backed up by any country’s central bank or government.

Volatility is statistical measure of dispersion for a given market index.

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Statement of problem

Little research has been done on the volatility of the bitcoin value.

There is minimal use of bitcoin both as currency and as an investment worldwide.

It is a relatively new form of currency, hence people are not familiar with it.

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Research objectives

Main Objective:-Forecasting return of the Bitcoin/USD exchange rate.

Specific Objective Identify drivers of exchange rate volatility. To model ARCH effects of the data. To compare model performance using AIC.

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Justification

This study will benefit:

I. Investors in financial Markets:- A decision-making tool with respect to risk level.

II. Researchers:- This paper offers further insight for literature review.

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LITERATURE REVIEW

Sakoshi Nakamoto (2008) came up with a paper on what bitcoin is and how it operates.

Bollerslev (1986)proposed an extension of ARCH(GARCH) which reduces parameters in order to forecast volatility and reduces weight. It is also claimed to be the most robust (Engel, 2001) and outperformed by none.

Straole (2014) fitted a modified GARCH(1,1) model by adding some identified variables to the conditional variance equation. 6

METHODOLOGY Convert BTC/USD exchange rate data to logarithmic

returns and plot time series to check for volatility clustering.

Test for Normality using Jarque Bera (JB). Here tests for skewness and Kurtosis are carried out.

Test for stationarity of the data using Augmented Dickey Fuller test.

∆yt = ∂yt-1 + ut Test for ARCH Effects using LM-test.

• is the daily return• and are the exchange rates of

the current day and previous day respectively.

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CONT’D Use Pearson’s Product Moment test to check collinearity. A GARCH (p,q) process has conditional variance described as follows:-

Where;

Use AIC values to identify the best volatility model.Where k is

degrees of freedom

The GARCH model is then evaluated using Ljung-Box Test Statistic.

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EMPIRICAL ANALYSIS AND RESULTSA time series plot shows that large changes tend to be followed by large changes and small changes tend to be followed by small changes.

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Cont’d The Jacque Bera tests show hat the returns have excess kurtosis

(10.5889) and positive skewness.

The ADF test statistic is -9.8383 showing that the process has no unit roots, thus rejecting the null hypothesis.

Test for arch effects is established to have a p-value of less than 0.05 hence arch effects are present and reject null hypothesis which states that there are no ARCH effects in the data.

Test-Statistic p.value297.8466 0

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Pearson’s Correlation tests.Variable Test Price

ReturnsTrade Volume

World Index

Price Returns

Pearson’s 1 -0.02990395 -0.044

Significance 2-tailed

.000 0.173

Trade Volume

Pearson’s -0.02990395 1 0.011

Significance 2-tailed

.000 .744

World Index Pearson’s -0.044 0.011 1

Significance 2-tailed

.173 .744

None of the other variables displays any significant correlation with each other. Price returns and Trade volume are significant factors.

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Volatility Analysis

The plot tails off.

We plot pacf and acf plots to obtain significant lags, which will guide on the q and p orders respectively.

The process tails off at 10. Lags 1, 2, 4 and 5 are significant at 5% interval.

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Model Specification Using the results from the ACF and PACF plots, several GARCH models are fitted. Some are tabulated as shown below.

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GARCH(P,Q) Mu Omega Alpha0 Alpha1 Alpha2 Beta1 Beta2 Beta3

GARCH(1,1) 1.357210*-03

2.390210*-05

2.43210*-05

3.318410*-01

- 7.404410*-01

- -

GARCH(2,2) 1.414210*-03

4.048810*-05

1.99610*-05

2.888110*-01

2.674410*-01

1.123410*-01

4.532410*-01

-

GARCH(1,3) 1.407710*-03

2.629210*-05

2.53310*-05

3.697910*-01

- 6.443910*-01

1.000010*-08

6.483610*-02

Choosing the Best Model

Variable GARCH(1,1) 

GARCH(2,2) 

GARCH(1,3)

AIC Value -3.654902 -3.654543 -3.654392

AIC values for different GARCH(p,q) models are compared. The best three models are shown below.

The GARCH (1,1) model gives the least values in terms of AIC hence selected as the best model.The researchers checked for model adequacy by the use of Ljung Box test on residuals. The p.value is greater than 0.05 (0.08827), hence fail to reject the null hypothesis that there is no serial correlation and thus the residuals are randomly distributed.

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Forecasting Using GARCH(1,1)

The actual return is 0.0046838493, which is within the confidence interval. The difference could be due to other exogenous variables on volatility such as trade volume.

Mean Forecast Standard Deviation Lower Interval Upper Interval

-0.0004826701 0.03018104 -0.05963643 0.05867109

-0.0004826701 0.03186329 -0.06293358 0.06196824

-0.0004826701 0.03348398 -0.06611006 0.06514472

-0.0004826701 0.03505196 -0.06918325 0.06821791

-0.0004826701 0.03657433 -0.07216704 0.07120170

-0.0004826701 0.03805687 -0.07507277 0.07410742

-0.0004826701 0.03950436 -0.07790979 0.07694445

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Forecast Plot

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A comparison of 1-step and 7-step forecast shows that the standard deviation increases with increase in h.

DISCUSSIONS AND CONCLUSIONS There is presence of volatility clustering in the returns implying that

shocks today will impact the expectation of volatility several periods ahead.The returns exhibit excess kurtosis and positive skewness, which is common for financial data.

GARCH(1,1) gives the least AIC value hence picked for modelling and forecasting returns. This is backed by the difference between the actual and forecast being small (0.003326677312426).

The residuals of the GARCH(1,1) model are uncorrelated, hence the assumption has been proved.

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RECOMMENDATION The researchers recommend use of other

volatility models such as EGARCH and further studies on other aspects of Bitcoin.

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REFERENCES Nakamoto (2008) A peer to peer. Bollerslev, T. (1986). Generalized autoregressive conditional

heteroskedasticity. Journal of Econometrics. Poon, S.H & Granger, C.(2003). Forecasting Volatility in Financial

Markets: A Review. Journal of Economic Literature,41,478-539. Wallace, Benjamin. "The Rise and Fall of Bitcoin." Wired.com. Conde

Nast Digital, 23 Nov. 2011. Web. 05 May 2012 Murphy, R. P. (2003) The Origin of Money and its Value. Mises Daily https://www.quandl.com Yermack, D. (2014, April 1). Is Bitcoin a real currency? An economic

appraisal. [Working Paper] New York: University Stern School of Business and National Bureau of Economic Research.

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Thank You!

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