Sains Malaysiana 49(3)(2020): 703-712
http://dx.doi.org/10.17576/jsm-2020-4903-25
Modeling
the Volatility of
Cryptocurrencies: An Empirical Application of
Stochastic Volatility Models
(Pemodelan Kemeruapan Mata Wang Kripto:
Pengaplikasian Empirik
Model Kemeruapan Stokastik)
MAMOONA ZAHID & FARHAT IQBAL*
Department
of Statistics, University of Balochistan,
Quetta, Pakistan
Diserahkan: 8 April 2019/Diterima: 10 November 2019
ABSTRACT
This paper compares
a number of stochastic volatility (SV) models for modeling and predicting
the volatility of the four most capitalized cryptocurrencies (Bitcoin,
Ethereum, Ripple, and Litecoin).
The standard SV model, models with heavy-tails and moving average
innovations, models with jumps, leverage effects and volatility
in mean were considered. The Bayes factor for model fit was largely
in favor of the heavy-tailed SV model. The forecasting performance
of this model was also found superior than the other competing models.
Overall, the findings of this study suggest using the heavy-tailed
stochastic volatility model for modeling and forecasting the volatility
of cryptocurrencies.
Keywords:
Bayesian model comparison; cryptocurrency; jumps; leverage; stochastic volatility
ABSTRAK
Kertas ini membandingkan
beberapa model kemeruapan stokastik (SV) untuk pemodelan danpenganggaran kemeruapan empat modal mata wang kripto
(Bitcoin,
Ethereum, Ripple dan Litecoin). Model standard SV, model dengan hujung
berat dan inovasi purata pergerakan, model dengan lompatan, kesan pengaruh dan kemeruapan dalam min diambil kira. Faktor Bayes untuk model penyuaian selalunya menyebelahi
model SV hujung berat. Prestasi peramalan model ini didapati superior daripada model lain yang dibandingkan. Secara keseluruhan, keputusan kajian ini mencadangkan penggunaan model kemeruapan stokastik hujung berat untuk
pemodelan penganggaran
kemeruapan mata wang kripto.
Kata kunci: Kemeruapan stokastik; lompatan; mata wang kripto; perbandingan model
Bayesi; pengaruh
RUJUKAN
Baur, D.G. & Dimpfl, T. 2018. Asymmetric volatility in crypto-currencies.
Economic Letters 173: 148-151.
Bezerra, P.C.S. & Albuquerque,
P.H.M. 2017. Volatility forecasting via SVR-GARCH with mixture of Gaussian kernels. Computational Management Science 14(2):
179-196.
Bollerslev, T. 1986. Generalized
autoregressive conditional heteroskedasticity.
Journal of Econometrics 31(3):
307-327.
Borri, N. 2019. Conditional
tail-risk in cryptocurrency markets. Journal of Empirical Finance
50: 1-19.
Bouri, E., Azzi, G. & Dyhrberg, A.H. 2017.
On the return-volatility relationship in the Bitcoin market around
the price crash of 2013. Economics:
The Open-Access, Open-Assessment E-Journal 11: 1-16.
Caporale, G.M. & Zekokh, T. 2019. Modelling volatility of cryptocurrencies
using markov-switching GARCH models. Research
in International Business and Finance 48: 143-155.
Catania, L. &
Grassi, S. 2017. Modelling crypto-currencies financial time-series.
CEIS Working Paper No. 417. Available at SSRN: https://ssrn.com/abstract=3084109.
Catania, L., Grassi, S. & Ravazzolo, F. 2018.
Predicting the volatility of cryptocurrency time-series. CAMP Working Paper Series 3.
Chan, J.C.C. 2015.
The stochastic volatility in mean model with time-varying parameters:
An application to inflation modelling. Journal
of Business and Economic Statistics 35(1): 17-28.
Chan, J.C.C. 2013.
Moving average stochastic volatility models with applications to
inflation forecast. Journal
of Econometrics 176(2): 162-172.
Chan, J.C.C. &
Grant, A.L. 2016. Modeling energy price dynamics: GARCH versus stochastic
volatility. Energy Economics
54: 182-189.
Chan, J.C.C. &
Eisenstat, E. 2015. Marginal likelihood
estimation with cross-entropy method. Economics
Review 34(3): 256-285.
Chan, J.C.C. &
Jeliazkov, I. 2009. Efficient simulation
and integrated likelihood estimation in state space models. International Journal of Mathematical Modelling and Numerical Optimisation 1: 101-120.
Charfeddine, L. & Maouchi, Y. 2018. Are shocks on the returns and volatility
of cryptocurrencies really persistent? Finance Research Letters
28: 423-430.
Charle, A. & Darne-Lemna, O. 2018. Volatility estimation for bitcoin: Replication
and robustness. International Economics 157: 23-32.
Cheong, C.W., Lai,
N.S., Isa, Z. & Nor, A.H.S.M. 2012. Asymmetry dynamic volatility
forecast evaluations using interday and
intraday data. Sains Malaysiana 14(10): 1287-1299.
Chu, J., Chan, S.,
Nadarajah, S. & Osterrieder,
J. 2017. GARCH modelling of cryptocurrencies. Journal of Risk and Financial Management 10(4): 17. doi:10.3390/jrfm10040017.
Creal, D., Koopman, S.J. & Lucas, A. 2013. Generalized autoregressive
score models with applications. Journal of Applied Econometrics 28(5): 777-795.
Diebold, F.X. &
Mariano, R.S. 1995. Comparing predictive accuracy. Journal of Business and Economic Statistics 13(3): 253-263.
Eraker, B., Johannes, M.
& Polson, N. 2003. The impact of jumps in volatility and returns. Journal of Finance 58(3): 1269-1300.
Fakhfekh, M. & Jeribi, A. 2020. Volatility dynamics of crypto-currencies’
returns: Evidence from asymmetric and long memory GARCH models.
Research in International Business and Finance 51: 101075.
Ghysels, E., Harvey, A.C.
& Renault, E. 1996. Stochastic volatility. In Statistical Models in Finance,
edited by Rao, C.R. & Maddala, G.S.
North-Holland, Amsterdam; Elsevier. pp. 119-191.
Gkillas, K. & Katsiampa, P. 2018. An application
of extreme value theory to cryptocurrencies. Economics Letters 164: 109-111.
Harvey, A.C. 2013.
Dynamic Models for Volatility
and Heavy Tails: With Applications to Financial and Economic Time
Series. Volume 52. New York: Cambridge University Press.
Harvey, A.C. &
Shephard, N. 1996. The estimation of an
asymmetric stochastic volatility model for asset returns. Journal of Business and Economic Statistics 14: 429-434.
Harvey, D., Leybourne, S. & Newbold, P. 1997. Testing the equality
of prediction mean squared error. International
Journal of Forecasting 13(2): 281-291.
Katsiampa, P. 2017. Volatility
estimation for bitcoin: A comparison of GARCH models. Economics Letters 158: 3-6.
Koopman, S.J. & Hol Uspensky, E. 2002. The stochastic volatility in mean model: Empirical
evidence from international stock markets. Journal of Applied Econometrics 17(6): 667-689.
Liesenfeld, R. & Jung,
R.C. 2000. Stochastic volatility models: Conditional normality versus
heavy-tailed distributions. Journal
of Applied Econometrics 15: 137-160.
Liu, R., Shao, Z.,
Wei, G. & Wang, W. 2017. GARCH model with fat-tailed distributions
and bitcoin exchange rate returns. Journal
of Accounting, Business and Finance Research 1(1): 71-75.
Naimy, V.Y. & Hayek,
M.R. 2018. Modelling and predicting the bitcoin volatility using
GARCH models. International
Journal of Mathematical Modelling and Numerical Optimisation
8(3): 197-215.
Peng, Y., Albuquerque,
P.H.M., de Sa, J.M.C., Padula, A.J.A.
& Montenegro, M.R. 2018. The best of two worlds: Forecasting
high frequency volatility for cryptocurrencies and traditional currencies
with support vector regression. Expert
Systems with Applications 97: 177-192.
Rahim, M.A.A., Zahari, S.M. & Shariff, S.R.
2018. Variance targeting estimator for GJR-GARCH under Model’s Misspecification.
Sains Malaysiana
47(9): 2195-2204.
Shephard, N. 1996. Statistical
aspects of ARCH and stochastic volatility. In Time Series Models in Econometrics, Finance and Other Fields, edited
by Cox, D.R., Hinkley, D.V. & Barndorff-Nielson, O.E. London: Chapman & Hall. pp. 1-67.
Stavroyiannis, S. & Babalos, V. 2017. Dynamic Properties of the Bitcoin and
the US market. Accessed
May 10, 2018. https://ssrn.com/abstract=2966998.
Taylor, S.J. 1986.
Modelling Financial Time Series.
Chichester: John Wiley.
Urquhart,
A. 2017. The volatility of Bitcoin.
SSRN Electronic Journal. DOI: 10.2139/ssrn.2921082.
*Pengarang untuk surat-menyurat; email: farhatiqb@gmail.com
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