Long memory investigation and application of wavelet decomposition to improve the performance of stock market volatility forecasting

Because of very large frequency and volatility in Financial markets Indicators, a certain type of non stationary is created that it refers to the fraction non stationary. This causes, provides Long memory in this type of time series. Hence, this study has in addition to examine the existence of the long memory in both mean and variance equations in the return series of Tehran stock exchange, Pays to forecasting the volatility of this index. For this purpose, the daily data from fifth Farvardin 1388 to eighteenth Ordibehesht 1391 is used. Our results confirm the existence of Long Memory in both mean and variance equations. However, among others, based on the information criteria and MSE, ARFIMA (1,2)-FIGARCH(BBM) model has been selected as the best specification to model and forecast the volatility of Tehran stock exchange’s return. As well, in order to Forecasting the volatility of this series, was used Combination of the above model with Level and decomposed data. The results show that, according to the forecasting error criteria (MSE and RMSE), the result of model’s based on decomposed data (with wavelet technique), more acceptable.