Estimate AR(3) by Using Levinson-Durbin Recurrence & Weighted Least Squares Error Methods

Abstract

In this study, we investigate about the estimation improvement for Autoregressive model of the third order, by using Levinson-Durbin Recurrence (LDR) and Weighted Least Squares Error ( WLSE ).By generating time series from AR(3) model when the error term for AR(3) is normally and Non normally distributed and when the error term has ARCH(q) model with order q=1,2.We used different samples sizes and the results are obtained by using simulation. In general, we concluded that the estimation improvement for Autoregressive model for both estimation methods (LDR&WLSE), would be by increasing sample size, for all distributions which are considered for the error term , except the lognormal distribution. Also we see that the estimation improvement for WSLE method, depends on the value for the Forgetting Factor parameter (α),which haave value less than one(i.e. 1) ( α< ). The estimate is improved for large value for parameterα exactly at 0.99 α= .Finally, we used the estimation methods (LDR&WLSE) for real data.