以上证综指的5min高频数据为例,在已有的多分形波动率(multifractal volatility)测度方法基础上,提出了新的波动率测度方法及模型.运用滚动时间窗的样本外预测技术以及比SPA检验更具优势的“模型信度设定检验”(model confidence set,MCS),对比了新的波动率测度模型和主流的GARCH族以及已实现波动率(realized volatility)模型的预测精度.实证结果显示:不论是短记忆模型还是长记忆模型,多分形波动率模型的预测精度明显优于GARCH族模型,且长记忆模型的预测能力要好于短记忆模型.同时,在多数损失函数下,新提出的多分形波动率测度方法及其动力学模型的预测效果都是最优的.
This paper introduces a new volatility measure and constructs its model based on multifractal volatil- ity method. Taking 5-minute high frequency data of the Shanghai Composite Index as an example, and applying the out-of-sample rolling time window forecasting combined with Model Confidence Set which is proved superior to SPA test, this paper compares the empirical performance of the new model and those of the GARCH- type and Realized volatility (RV) models. The empirical results show that the forecasting accuracy of the mul- tifractal volatility measure model in the short term as well as in the long term are better than the GARCH-type and RV models. Moreover, the forecasting models in the long term perform better than those in the short term. The performance in most loss function of the new method based on muhifractal volatility measure is superior to other forecasting models.