证券市场指数加权移动平均多重分形波动率模型

Multifractal Volatility Forecast Model Based on Exponentially Weighted Moving Average of Securities Market in China

针对现有的多重分形波动率修正因子的不足,将指数加权移动平均建模思想应用于多重分形波动率建模,构建了指数加权移动平均多重分形波动率模型(EMFV)。从样本拟合结果、样本外波动率预测精度以及VaR预测能力三个维度上考察了多重分形波动率测度及其动力学模型的效果。基于改进后的EMFV模型,在样本内有更好的拟合效果,在样本外的波动率预测效果上,ARMA-EMFV模型和HAR-EMFV模型有更小预测误差。考察其对VaR值的预测效果,发现基于改进波动率测度EMFV建立起来ARFIMA模型和HAR模型在预测VaR精度上,都要比原来的MFV效果更好,说明改进的波动率测度对金融市场波动有更加显著的刻画能力。并且在空头VaR预测水平上,基于多重分形波动率测度模型比GARCH类模型效果更优。最后给出了EMFV的参数β值与波动率预测误差的关系。

A new method for improving the measurement of multifractal volatility is proposed in this paper. This paper constructs Exponentially Weighted Moving Average Multifractal volatility index(EMFV). The empirical result shows that the new multifractal volatility measure owns a better model fitting ability, with less error in the prediction outside the sample. In addition, the paper applies the model to VaR prediction, as ARFIMA model and HAR model established by EMFV are better than the MFV in predicting VaR accuracy. Moreover, the model based on multifractal volatility is better than the traditional GARCH model in most short VaR prediction. Finally, the relationship between beta and volatility prediction error is discussed.