Statistical modelling of Bitcoin volatility : Has the sanctions on Russia had any effect on Bitcoin?

Abstract: This thesis aims to fit and compare different time series models namely the ARIMA-model, conditional heteroscedastic models and lastly a dynamic regression model with ARIMA error to Bitcoin closing price data that spans over 5 consecutive years. The purpose is to evaluate if the sanction on Russia had any effect on the cryptocurrency Bitcoin. After giving a very brief introduction to time series models and the nature of the error term, we describe the models that we want to compare. Quite early in on, autocorrelation was detected and that the time series were nonstationary. Additionally, as we are dealing with financial data, we found that the best alternative was to transform the data into logarithmic return and we then took the first difference. As we then detected a very large outlier, we decided to replace the extreme value with the mean of the two adjacent observations as we suspected it would affect the forecast interval. The dataset with first differenced log-returns was used in the ARIMA model but it turned out that there was no autocorrelation which indicated that returns in financial assets are uncorrelated across time and therefore unpredictable. The conditional heteroscedastic models, the ARCH and the GARCH models turned out to be best suitable for our data, as there was an ARCH-effect present. We could conclude that the GARCH(1,1) model using student t-distribution had the best fit, which had the lowest AIC and the highest log likelihood. In order to study the effect of the sanctions on Bitcoin volatility a dynamic regression model was used by allowing the error term to contain autocorrelation and include an independent dummy variable. The model showed that the Russian invasion of Ukraine did not, surprisingly, have any effect on the Bitcoin closing price.