Estimation of the Difference Parameter in ARFIMA Models Using Parametric and Semi Parametric Methods

This paper investigates the persistence of the long memory property in the daily stock index EGX30. The long memory property of the series has been examined and a fractionally integrated autoregressive moving average (ARFIMA) model has been fitted using some parametric and semi parametric methods. Long memory has been scrutinized by Rescaled Range statistic (R/S), Aggregated Variance, and Absolute Moment. For the estimation of the model, the Geweke and Porter-Hudak’s) GPH), the Reisen’s (SPR), and the Local Whittle (LW) has been used as semi-parametric methods and Maximum Likelihood (MLE), Exact Maximum Likelihood (EML), Modified Profile Likelihood (MPL) and Conditional Sum of Squares (CSS) as parametric methods