Dynamic Volatility Modelling of Bitcoin Using Time-Varying Transition Probability Markov-Switching GARCH Model

Bitcoin (BTC), as the dominant cryptocurrency, has attracted tremendous attention lately due to its excessive volatility. This paper proposes the time-varying transition probability Markov-switching GARCH (TV-MSGARCH) models incorporated BTC logarithmic daily trading volume or Google daily searches as exogenous factors to model the volatility dynamics of BTC return series. Extensive comparisons were carried out to evaluate the modelling and forecasting performances of TV-MSGARCH models with the benchmark models such as GARCH, GJRGARCH, threshold GARCH and constant transition probability MSGARCH. Results reveal that the TV-MSGARCH models predominate other models for the in-sample model fitting based on log-likelihood function and other benchmark criteria. Furthermore, the TV-MSGARCH model with Google daily searches offers the best out-of-sample forecast evaluated based on quasi-likelihood loss function and also using Hansen's model confidence set. In addition, the Filardo's weighted transition probabilities is computed and the results show the existence of time-varying effect on transition probabilities. Lastly, new approach for computing different levels of long and short positions of value-at-risk forecasts based on TV-MSGARCH models are also provided and tested