This is a presentation on my undergraduate thesis on how to perform descriptive statistics, modelling and forecasting volatility to predict returns

1. FORECASTING THE
RETURN OF BITCOIN
EXCHANGE RATE
LYDIA NJERI NDUTA-SC283-2872/2011
SUZZY BUTEMBU LAVENTA-SC283-2915/2011
SUPERVISOR: DR. A. WAITITU

2. 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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3. 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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4. 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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5. 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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6. 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.
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7. METHODOLOGY
 Convert BTC/USD exchange rate data to logarithmic returns
and plot time series to check for volatility clustering.
𝑟𝑡= ln
𝑝𝑡
𝑝𝑡−1
 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.
• rt is the daily return
• pt and pt−1 are the exchange rates of
the current day and previous day
respectively.
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8. CONT’D
 Use Pearson’s Product Moment test to check collinearity.
 A GARCH (p,q) process has conditional variance described as follows:-
𝜎𝑡
2
= 𝛼0 +
𝑖=1
𝑝
𝛼𝑖 ∈ 𝑡−𝑖
2
+
𝑗=1
𝑞
𝛽𝑗 𝜎𝑡−𝑗
2
Where;
𝛼0 > 0, 𝛼𝑖 ≥ 0, 𝛽𝑗 ≥ 0
 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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9. EMPIRICAL ANALYSIS AND RESULTS
A 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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10. 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.value
297.8466 0
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11. Pearson’s Correlation tests.
Variable Test Price Returns Trade 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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12. 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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13. 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*-
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14. 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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15. 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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16. 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.

17. 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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18. RECOMMENDATION
 The researchers recommend use of other
volatility models such as EGARCH and further
studies on other aspects of Bitcoin.
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19. 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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20. Thank You!
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