GARCH and GAS: Comparison of volatility models for Bitcoin in different exchanges

Abstract

Different characteristics of cryptocurrencies have been investigated by a number of studies. In this study, I focus on conditional volatility of Bitcoin in three exchanges which are Coinbase, Bitfinex and Bitstamp. I investigate in-sample and out-of-sample performance of GARCH, GAS, Realized GARCH, GJR and EGARCH, and assess existence of inverse leverage effect. Moreover, multivariate GAS model with equi-correlation and constant correlation structures is applied. I find that, in the time period of this study, inverse leverage effect does not exist, and Normal GARCH-GAS model performs relatively better for out of sample forecasts. Furthermore, in multivariate part, I show that constant correlation t-GAS out performs other models with respect to AIC and BIC, and that estimated correlations, which are very close to one, provide evidence that while arbitrage opportunities exist across different markets, investors cannot diversify by investing in different markets.