Time series analysis of Cryptocurrency returns and volatilities

There is a significant interest in the growth and development of cryptocurrencies, the most notable ones being Bitcoin and Ripple. Global trading in these cryptocurrencies has led to highly speculative and "bubble-like" price movements. Since these cryptocurrencies trade like stocks, provide a feasible alternative to gold and appreciate during uncertain times, it can be hypothesized that their prices are partly determined by the global stock indices, gold prices, and fear gauges such as the VIX and the US Economic Policy Uncertainty Index. In this paper, we test this hypothesis by conducting a time series analysis of returns and volatilities of Bitcoin and of Ripple. We use the Autoregressive-moving-average model with exogenous inputs model (ARMAX), Generalized Autoregressive Conditionally Heteroscedastic (GARCH) model, Vector Autoregression (VAR) model, and Granger causality tests to determine linkages between returns and volatilities of Bitcoin and of Ripple. We find that the Bitcoin crash of 2018 could have been explained using these time series methods. We also find that returns of global stock markets and of gold do not have a causal effect on Bitcoin returns, but we do find returns on Ripple have a causal effect on Bitcoin prices.