Long Memory And Prediction Of Stock Market Volatility Based On WRV-ARFIMA-T Model

With the rapid development of the economy,the volatility characteristics of financial markets have become more and more complicated.In order to reduce the adverse effects of financial market volatility,a large number of financial scholars and investors have analyzed and researched on the volatility of the financial market.It is necessary for volatility to construct a model that matches the characteristics of the volatility itself,which effectively describe and predict.In practical applications,volatility of high-frequency financial data often has the characteristics of calendar effect,peak thick tail and long memory.It is necessary to adopt a model that can capture these characteristics at the same time.In addition,it is difficult to estimate the parameters of time series models directly by using the classical frequency statistics method because the likelihood function necessarily has not an analytical expression.Therefore,this paper constructs a weighted realized volatility autoregressive fractional integrated moving average(WRV-ARFIMA-T)model with T-distributed innovations.The bayesian estimation method is used to estimate the parameters of the model,and empirical research on the volatility of high-frequency financial data in China's stock market.The specific item is as follows:1.Considering that the volatility of high-frequency financial data has the characteristics of calendar effect,peak thick tail and long memory,this paper combines the weighted realized volatility(WRV)that can eliminates calendar effect and the autoregressive fractional integrated moving average(ARFIMA-T)model with T-distributed innovations that can depict the peak thick tail and long memory,thus constructing the WRV-ARFIMA-T model.To better describe and predict the volatility of high-frequency time series data,the bayesian estimation method is applied to estimate the parameters of the model.Then the statistical structures of WRV and ARFIMA-T models are analyzed,and the basic steps of Markov Chain Monte Carlo(MCMC)method for WRV-ARFIMA-T models are given.2.The WRV-ARFIMA-T model and bayesian estimation method are used to empirically study the long memory and prediction of the volatility of high-frequency financial data in China's stock market.With the help of Matlab,Eviews,OpenBUGS and other software,the WRV series of CSI 300 index and SME index in China's stock market are verified to have the qualities of peak thick tail and long memory by using Q-Q graph,auto-correlation function graph and multiple range(R/S)analysis method.Next,the WRV-ARFIMA-T model is established for the WRV series of these two indices.Meanwhile the parameters of the model are estimated by the Bayesian estimation method.Finally,the WRV-ARFIMA(1,0.4914,3)-T model and WRV-ARFIMA(4,0.4881,1)-T model via the CSI 300 index and SME index are used to predict the weighted realized volatility.The results show that the model has better prediction accuracy.