This study is an attempt to review the theory and applications of autoregressive fractionally integrated moving average (ARFIMA) and fractionally integrated generalized autoregressive conditional heteroskedasticity (FIGARCH) models, mainly for the purpose of the description of the observed persistence in the mean and volatility of a time series. The long memory feature in FIGARCH models makes them a better candidate than other conditional heteroskedasticity models for modeling volatility in financial series. ARFIMA model also has a considerable capacity for modeling the return behavior of these time series. The daily data related to Tehran Stock Exchange (TSE) index was used for the purpose of this study. Considering the fact that the existence of conditional heteroskedasticity effects were confirmed in the stock return series, robust regression technique was used for estimation of different ARFIMA models. Furthermore, different GARCH-type models were also compared. The results of ARFIMA model are indicative of the absence of long memory in return series of the TSE index and the results from FIGARCH model show evidence of long memory in conditional variance of this series.
