Forecasting Bitcoin Prices Movements: Memory, Path Dependence and Persistence

Being able to predict changes in Bitcoin prices is purportedly a boon for risky investors, more so, if the forecasts are largely unconditional and can only be explained by the series’ own historical trajectories. Although memory dynamics have been exploited in forecasting changes in prices, Bitcoin markets pose additional challenges, because the lack of proper financial theoretic model limits the development of adequate theory-driven empirical construct. In this paper, we propose a class of autoregressive fractionally integrated moving average (ARFIMA) model with asymmetric exponential generalized autoregressive score (AEGAS) or exponential GAS with leverage effect (EGAS-L) errors to accommodate a complex interplay of ‘memory’ to drive predictive performance (an out-of-sample forecasting). Our conditional variance includes leverage effect, jumps and fat tail-skewness distribution, each of which affects magnitude of memory the Bitcoin price system would possess. This enables us to build a true forecast function. We estimate several models using the Skewed Student-t maximum likelihood and find that the informational shocks, in general, have permanent effects on Bitcoin price changes. We show that this model has better predictive performance over competing models. The prediction from this model beats comfortably the random walk model. Accordingly, we find that the weak efficiency assumption of cryptocurrency markets stands violated over a long period.