Research On Realized Volatility Based On Wavelet Analysis

Volatility is a very important variable in finance.It plays an important role in asset pricing,risk management and portfolio.So how to describe the volatility for financial asset accurately to make a prediction becomes one of the focus for international and domestic scholars.Also this is the major research object for both large investment organizations and individual investors.Although domestic and international scholars have made many achievements in this field,during the Interrelations of literatures found that there still exist two issues:(1)Although it is more and more convenient for the acquisition of high-frequency data,most of the scholars still use the time series made by low-frequency data based on day level for research,so that they may ignore the abundant information in high-frequency data.(2)Wavelet analysis which called “mathematical microscope” is now widely used in non-financial field and also has made good effect.But most of the volatility research using the whole time series to model and analyze then to predict instead of using time-frequency double dimension to excavate the useful information.Based on the issues,this article tries to set the high-frequency data in 5 minutes closing price of HS300 index as base data and introduce wavelet analysis to research.In order to verify whether wavelet analysis can improve the prediction accuracy,this article designed three method to compare the different RMSE,MAE,MAPE to judge the effect.The first method: using the high-frequency data as base to calculate RV,then build ARFIMA-RV model and predict the volatility.Record the index RMSE,MAE,MAPE to be reference standard.The second method: Using wavelet analysis to de-noise the high-frequency data and recalculate RV,then set ARFIMA-RV model based on them and predict the volatility.Record the index RMSE,MAE,MAPE.The third method: Using wavelet multi-frequency analysis to 3-MODWT RV,then get the 3 high-frequency series and 1 low-frequency series which represents different frequency,reproduce the steps of calculating VaR.Build ARFIMA-RV model and predict separately,then accumulate the predicted value of each subsequence to get the final predicted values.Record the index RMSE,MAE,MAPE.The comparison of RMSE,MAE,MAPE indicates that the prediction accuracy of volatility is improved after the introduction of wavelet analysis.Especially the third method has the best effect.Finally apply the volatility estimation value to the calculation of VaR.In the T distribution and 95%,97%,99% three different confidence level,Va R models all passed the kupiec failure inspection.This shows that the wavelet analysis can improve the accuracy of volatility prediction and the volatility also has practical significance,such as used in calculating VaR.