【摘要】 考虑日间波动的多重分形性、时变性及异方差性，构建了HAR-HV、HAR-FV、HAR-BSMFV和HAR-TSMFV模型，评价并比较了这4种HAR族模型的拟合优度和预测精度。实证结果和MCS检验证实，引入马尔可夫转换多重分形波动的HAR-SMFV类模型的预测能力显著提高且结果具有稳健性，其中HAR-TSMFV模型不仅刻画了日间波动的时变性和异方差性，而且捕捉了3种多重分形波动之间的转换，表现出最高的预测精度。更多还原

【Abstract】 Considering the multi-fractal, time-varying and heteroscedasticity of daytime volatility, this paper constructs HAR-HV, HAR-FV, HAR-BSMFV and HAR-TSMFV models and evaluates and compares the goodness of fit and prediction accuracy of these four HAR models. The empirical results and the MCS test confirm that the HAR-SMFV models with Markov-switching multi-fractal volatility have significantly improved predictive abilities and the results are robust. Among them, the HAR-TSMFV model not only describes the time-varying and heteroscedasticity of daytime volatility, but also captures the conversion between the three multi-fractal volatility forms, showing the highest prediction accuracy.更多还原