Forecasting Stock Market Volatility With Realized Volatility And Multifractal Volatility Method

Stock market volatility is a basic and important issue in financial researches.The stock volatility research is of great theoretical significance and practical needs for derivative pricing,portfolio,price prediction and financial risk supervision.In this paper,we use total 1389 trading days' daily and 5min high frequency data of the CSI 300 Index between April 15 2010 and December 31 2015 as a sample.According to the fluctuation patterns of different period of the sample interval,we divide the sample into two parts.After then,we use the Ljung-Box test,R/S method,DFA method to research samples' statistical characteristics in different periods.After analysis samples' complex nonlinear characteristics,this paper will continue to be the following:First,we build two realized volatility indicators and five multifractal volatility indicators based on high frequency data.After that,we set four kinds of GARCH model,two kinds of realized volatility and five kinds of multifractal volatility ARMA model,take sequence fitting,model parameter estimation and diagnostic testing.Second,in each period,we divide sample data into two parts:one is estimating sample,the other is remaining sample.With the "rolling time windows" technique,we adopt the out-of-sample forecast method on these models.Third,we apply the loss function method,SPA test and MCS test to analysis the deviation between the model forecasting values and four real volatility agent variables,and compare the predictive ability of these models.Empirical research shows that,the realized volatility models and the multifractal volatility models have excellent forecast capacity than GARCH family models.The realized volatility models have the best fitting and predictive ability in the whole period and the period ?.Multifractal volatility models have the best fitting and predictive ability during the gentle fluctuation period ?.