Time Series Analysis of Bitcoin

This thesis addresses the prediction problems associated with noncausal processes in cryptocurrency markets. Chapter one provides background on Bitcoin and cryptocurrencies in general. It begins by introducing four major cryptocurrencies. Then recent developments in economic research on Bitcoin are discussed.

Chapter two introduces a noncausal autoregressive process with Cauchy errors in application to the exchange rates of the Bitcoin electronic currency against the US Dollar. The dynamics of the daily Bitcoin/USD exchange rate series display episodes of local trends, which are modelled and interpreted as speculative bubbles. The structure of the Bitcoin market is described to give context for the presence of multiple bubbles in the exchange rate. The bubbles may result from the speculative component in the on-line trading. The Bitcoin/USD exchange rates are modelled and predicted. The mixed causal-noncausal autoregressive model is shown to better fit the data than the traditional purely causal model. A forecasting exercise using the noncausal model is then presented.

Chapter three examines the performance of nonlinear forecasts of noncausal processes from closed-form functional predictive density estimators. To examine the performance, time series are simulated with different conditional means and non-Gaussian distributions. The processes considered have the mixed causal-noncausal MAR(1,1)dynamics and both finite and infinite variance. The forecasts are assessed based on the forecast error behaviour and the goodness of fit of the estimated predictive density. The persistence in the noncausal component directly relates to the magnitude of the bubble effects in the time series and is found to have a meaningful impact on how forecastable the process is. To better predict bubbles the joint density of the forecast at horizon two is shown to be an effective graphical method to detect the outset of a bubble.