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 with BTC daily trading volume and daily Google searches singly and jointly as exogenous variables to model the volatility dynamics of BTC return series. Extensive comparisons are carried out to evaluate the modelling performances of the proposed model with the benchmark models such as GARCH, GJRGARCH, threshold GARCH, constant transition probability MSGARCH and MSGJRGARCH. Results reveal that the TV-MSGARCH models with skewed and fat-tailed distribution predominate other models for the in-sample model fitting based on Akaike information criterion and other benchmark criteria. Furthermore, it is found that the TV-MSGARCH model with BTC daily trading volume and student-t error distribution offers the best out-of-sample forecast evaluated based on the mean square error loss function using Hansen’s model confidence set. Filardo’s weighted transition probabilities are also computed and the results show the existence of time-varying effect on transition probabilities. Lastly, different levels of long and short positions of value-at-risk and the expected shortfall forecasts based on MSGARCH, MSGJRGARCH and TV-MSGARCH models are also examined.

比特币（BTC）作为主要的加密货币，近来由于其过度波动而备受关注。本文提出了结合BTC每日交易量和Google每日Google搜索的时变转移概率马尔可夫转换GARCH（TV-MSGARCH）模型作为外生变量来建模BTC收益序列的波动动力学。进行了广泛的比较，以评估所提出模型与基准模型（例如GARCH，GJRGARCH，阈值GARCH，恒定转移概率MSGARCH和MSGJRGARCH）的建模性能。结果表明，基于Akaike信息准则和其他基准准则，具有偏态分布和肥尾分布的TV-MSGARCH模型在其他模型拟合中占主导地位。此外，我们发现，具有BTC每日交易量和Student-t误差分布的TV-MSGARCH模型提供了最佳的样本外预测，该预测是使用Hansen模型置信度集基于均方误差损失函数评估的。还计算了菲拉尔多的加权过渡概率，结果表明存在时变效应对过渡概率的影响。最后，还研究了基于MSGARCH，MSGJRGARCH和TV-MSGARCH模型的不同级别的风险价值多头和空头头寸以及预期的空头预测。还计算了菲拉尔多的加权过渡概率，结果表明存在时变效应对过渡概率的影响。最后，还研究了基于MSGARCH，MSGJRGARCH和TV-MSGARCH模型的不同级别的风险价值多头和空头头寸以及预期的空头预测。还计算了菲拉尔多的加权过渡概率，结果表明存在时变效应对过渡概率的影响。最后，还研究了基于MSGARCH，MSGJRGARCH和TV-MSGARCH模型的不同级别的风险价值多头和空头头寸以及预期的空头预测。