On the predictive power of ARJI volatility forecasts for Bitcoin

ABSTRACT

Motivated by the recent literature on cryptocurrency volatility dynamics, this paper adopts the ARJI, GARCH, EGARCH, and CGARCH models to explore their capabilities to make out-of-sample volatility forecasts for Bitcoin returns over a daily horizon from 2013 to 2018. The empirical results indicate that the ARJI jump model can cope with the extreme price movements of Bitcoin, showing comparatively superior in-sample goodness-of-fit, as well as out-of-sample predictive performance. However, due to the excessive volatility swings on the cryptocurrency market, the realized volatility of Bitcoin prices is only marginally explained by the GARCH genre of employed models.

KEYWORDS:

• Bitcoin
• cryptocurrency
• ARJI
• realized volatility

JEL CLASSIFICATION:

• C52
• C53
• G15

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ The Bitcoin price fluctuations referred to are based on price quotes from https://bitcoincharts.com/.

² Ciaian, Rajcaniova, and Kancs (2016) document that market forces and Bitcoin attractiveness to investors and users have a significant impact on Bitcoin prices, but with variation over time.

³ Bouri et al. (2017a) ascertain whether Bitcoin acts as a diversifier, hedge, or safe haven against daily movements of general and energy commodities. They find strong evidence that Bitcoin exhibits hedging and safe-haven properties for both commodity indices during the overall and pre-crash periods.

⁴ The ARJI model has been extensively tested and proven in empirical finance areas, including stock returns (Lee and Hung 2007; Su and Hung 2011), exchange rates (Chan 2004), and commodity prices (Chan and Young 2006; Gronwald 2012).

⁵ The squared daily return has been criticized as an exceedingly noisy estimator for latent volatility since it will be equal to zero if the closing prices are the same for two consecutive trading days even though it is highly volatile with widely fluctuating prices for some trading day.

⁶ Using the MZ regression, previous studies found evidence that the realized volatility can be explained by the forecasts of the GARCH(1,1) model ranging from 30% to 40% for stock market cases (e.g. Koopman, Jungbacker, and Hol 2005; Fuertes, Izzeldin, and Kalotychou 2009; Liu, Chiang, and Cheng 2012).

⁷ It falls outside the scope of this short paper to discuss the influence of the distributional specification on out-of-sample model performance. In fact, we have also conducted out-of-sample volatility forecasts for the four GARCH-type models with the student-t distribution employed in this study, which showed insignificant superiority to those under the normal distribution.