针对修正因子的不足,对多分形波动率进行了改进. 以改进的多分形波动率为中心,建立了考虑跳跃,杠杆效应等典型特征 的HAR 类波动模型.通过对上证综指高频数据进行分析,从模型拟合,预测和风险值预测三方面评价, HAR-L-lnMFV${}_t$-CJ 是最优的波动模型,且该模型优于传统的EGARCH-J模型和NGARCH-J 模型.这些研究说明了修正的多分形波动率测度是更为有效的波动估计量.

Aiming at the shortcomings of the correction factor, the paper adjusts the multifractal volatility measure. The model family for HAR with typical feature including jumps, leverage effect, etc., is set up, based on the center for modified multifractal volatility measure. By virtue of empirical analysis of high frequency data from Shanghai composite index, HAR-L-lnMFV${}_t$-CJ model is the optimal volatility model, according to evaluation criterion: Model goodness of fit, model forecasting and prediction of Value at Risk and this model outperforms traditional model: EGARCH-J and NGARCH-J. All of these studies illustrate that the modified multifractal volatility is a more effective volatility estimator.