Modelling the dynamics of Bitcoin and Litecoin: GARCH versus stochastic volatility models

ABSTRACT

We examine and compare a large number of generalized autoregressive conditional heteroskedastic (GARCH) and stochastic volatility (SV) models using series of Bitcoin and Litecoin price returns to assess the model fit for dynamics of these cryptocurrency price returns series. The various models examined include the standard GARCH(1,1) and SV with an AR(1) log-volatility process, as well as more flexible models with jumps, volatility in mean, leverage effects, t-distributed and moving average innovations. We report that the best model for Bitcoin is SV-t while it is GARCH-t for Litecoin. Overall, the t-class of models performs better than other classes for both cryptocurrencies. For Bitcoin, the SV models consistently outperform the GARCH models and the same holds true for Litecoin in most cases. Finally, the comparison of GARCH models with GARCH-GJR models reveals that the leverage effect is not significant for cryptocurrencies, suggesting that these do not behave like stock prices.

KEYWORDS:

• Bitcoin
• Litecoin
• cryptocurrency
• GARCH
• stochastic volatility

JEL CLASSIFICATION:

• C22
• G14
• G16

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ The Bitcoin bubble, The Economist, 1 November 2017.

² State of blockchain: Q4 2017, https://www.coindesk.com/research/state-blockchain-q4-2017/?slide=6.

³ Catching the bitcoin bug, The Economist, 14 April 2018.

⁴ Koop (2003) explains in detail the Bayesian model comparison.

⁵ We, however, could not model the leverage model for SV (SV-L) due to some convergence issues with the data.