A Modified Long Memory Model for Modeling Interminable Long Memory Process

Abstract

In this paper, Autoregressive Fractionally Integrated Moving Average (ARFIMA) model was modified and was used for modeling the daily Malaysia Stock Price Index (MSPI). The long and slow decline in autocorrelation function of the data showed the presence of Long Memory (LM) structure. Therefore, the Mandelbrot and Lo rescaled-range tests were used to test the presence of LM. The ARFIMA model then is further extend to the Autoregressive Fractionally Unit Root Integrated Moving Average (ARFURIMA) model. The Geweke and Porter-Hudak (GPH), Local Whittle Estimator (LWE), and Hurst Exponent (HE) were used as the estimation methods to obtain the LM parameters d of both ARFIMA and ARFURIMA models. The best model was identified for each of ARFIMA and ARFURIMA models respectively based on the minimum Akaike Information Criteria (AIC) values. The best fitted model were specified as ARFIMA (2,0.989,0) and ARFURIMA (1,1.069,0). Having compared the residuals analysis of the two models, we conclude that the ARFURIMA model was better in estimating series that exhibit Interminable LM (ILM).