Regime heteroskedasticity in Bitcoin: A comparison of Markov switching models

Chappell, Daniel (2018): Regime heteroskedasticity in Bitcoin: A comparison of Markov switching models.

Abstract

Markov regime-switching (MRS) models, also known as hidden Markov models (HMM), are used extensively to account for regime heteroskedasticity within the returns of financial assets. However, we believe this paper to be one of the first to apply such methodology to the time series of cryptocurrencies. In light of Molnar and Thies (2018) demonstrating that the price data of Bitcoin contained seven distinct volatility regimes, we will �fit a sample of Bitcoin returns with six m-state MRS estimations, with m between 2 and 7. Our aim is to identify the optimal number of states for modelling the regime heteroskedasticity in the price data of Bitcoin. Goodness-of-�fit will be judged using three information criteria, namely: Bayesian (BIC); Hannan-Quinn (HQ); and Akaike (AIC). We determined that the restricted 5-state model generated the optimal estimation for the sample. In addition, we found evidence of volatility clustering, volatility jumps and asymmetric volatility transitions whilst also inferring the persistence of shocks in the price data of Bitcoin.

• Item Type: MPRA Paper
• Language: English
• Keywords: Bitcoin; Markov regime-switching; regime heteroskedasticity; volatility transitions.
• Subjects: C - Mathematical and Quantitative Methods > C0 - General > C01 - Econometrics; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C26 - Instrumental Variables (IV) Estimation; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C50 - General

References

Alizadeh, A., Nomikos, N. and Pouliasis, P. (2008) A Markov regime switching approach for hedging energy commodities. Journal of Banking and Finance 32, 1970-1983.

Ang, A. and Timmermann, A. (2012) Regime Changes and Financial Markets. Annual Review of Financial Economics, 4, 313-337.

Ardia, D., Bluteau, K. and R�uede, M. (2018) Regime changes in Bitcoin GARCH volatility dynamics. Finance Research Letters. Available online: 10th August 2018.

Bai, X., Russell, R. and Tiao, C. (2003) Kurtosis of GARCH and stochastic volatility models with non-normal innovations. Journal of Econometrics, 114(2), 349-360.

Bauwens, L., Backer, B. and Dufays, A. (2014) A Bayesian method of change-point estimation with recurrent regimes: Application to GARCH models. Journal of Empirical Finance, 29, 207-229.

Bauwens, L., Preminger, A. and Rombouts, J. (2010) Theory and inference for a Markov switch GARCH model. Econometrics Journal, 13, 218-244.

Black, F. (1976) Studies of stock price volatility changes. In: Proceedings of the 1976 Meetings of the American Statistical Association, 171-181.

Bouoiyour, J. and Selmi, R. (2015) Bitcoin price: Is it really that new round of volatility can be on way? Munich Personal RePEc Archive, 6558.

Campbell, J., Lo, A. and Mackinlay, A. (1997) The Econometrics of Financial Markets, Princeton, NJ, Princeton University Press.

Chang,Y., Choi, Y and Park, J. (2017) A new approach to model regime switching. Journal of Econometrics, 196, 127-143.

Chu, J., Chan, S., Nadarajah, S. and Osterrieder, J. (2017) GARCH Modelling of Cryptocurrencies. Journal of Risk and Financial Management, 10, 17.

Dyhrberg, A. (2016a) Bitcoin, gold and the dollar A GARCH volatility analysis. Finance Research Letters, 16, 85-92.

Ghahramani, Z. (2001) An Introduction to Hidden Markov Models and Bayesian Networks. International Journal of Pattern Recognition and Artificial Intelligence, 15(1), 9-42.

Hamilton, J. (1989) A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle. Econometrica, 57, 357-384.

Hamilton, J. (1994) Time Series Analysis, Princeton, NJ, Princeton University Press.

Hamilton, J. and Susmel, R. (1994) Autoregressive conditional heteroskedasticity and changes in regime. Journal of Econometrics, 64, 307-333.

Henry, O. (2009) Regime switching in the relationship between equity returns and short-term interest rates in the UK. Journal of Banking and Finance 33, 405-414.

Katsiampa, P. (2017) Volatility estimation for Bitcoin: A comparison of GARCH models. Economics Letters, 158, 3-6.

Kim, C. (1994) Dynamic Linear Models with Markov-Switching. Journal of Econometrics, 60, 1-22.

Lamoureux, G. and Lastrapes, W. (1990) Heteroskedasticity in Stock Return Data:Volume versus GARCH Effects. Journal of Finance, 45, 221-229.

Langrock, R. MacDonald, I. L. and Zucchini, W. (2016) Hidden Markov Models for Time Series, 2nd ed., Boca Raton, FL, Taylor & Francis Group.

Mandelbrot, B. (1963a) The variation of certain speculative prices. Journal of Economic Literature, 30, 102-146.

Mandelbrot, B. (1963b) New methods in statistical economics. Journal of Political Economy, 71, 421-440.

Mandelbrot, B. (1967) The variation of some other speculative prices. Journal of Business, 40, 393-413.

Marcucci, J. (2005) Forecasting Stock Market Volatility with Regime-Switching GARCH models. Studies in Nonlinear Dynamics & Econometrics, 9(4).

Mizrach, B. (1990) Learning and Conditional Heteroskedasticity in Asset Returns. Mimeo, Department of Finance, The Warthon School, University of Pennsylvania.

Molnar, P. and Thies, S. (2018) Bayesian change point analysis of Bitcoin returns. Finance Research Letters, available online 20 March 2018.

Sims, C. and Zha, T. (2006) Were There Regime Switches in U.S. Monetary Policy?The American Economic Review, 96(1), 54-81.

Shaw, C. (2018) Conditional heteroskedasticity in crypto-asset returns. Journal of Statistics: Advances in Theory & Applications, (forthcoming).

Smith, R., Sola, M. and Spagnolo, F. (2000) The Prisoner's Dilemma and Regime-Switching in the Greek-Turkish Arms Race. Journal of Peace Research, 37(6), 737-750.

Stock, J. (1998) Estimating Continuous-Time Processes Subject to Time Deformation. Journal of the American Statistic Association, 83, 77-85.

Sun, P. and Zhou, C. (2014) Diagnosing the distribution of GARCH innovations.Journal of Empirical Finance, 29, 287-303.

Wilfling, B. (2009) Volatility regime-switching in European exchange rates prior to monetary uni�cation. Journal of International Money and Finance, 28, 240-270.