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Abstract
This thesis aims to introduce new forms of AR (P) model with constant. The first, second, third and fourth moments for the new forms AR AR (P) models are introduced and some of these moment are compared with the traditional moments which was introduce by Cochrane and Orcutt (1949). Furthermore, the (OLS) method is introduced to estimate the unknown parameters of AR (2) model without constant. On the other hand, the distribution of (OLS) estimator for AR (2) model without constant is derived. Also, the (WS) method is used to estimate the unknown parameters for AR (2) model with (without) constant. The properties of estimators are investigated theoretically. In addition, the estimation for AR (2) model for panel data with (without) constant are obtained using (OLS) method. Finally, a simulation study has been conducted to compare between different methods of estimation (OLS, WS and Vrbik) for different sample sizes (15, 30, 50, 100 and 200) for AR (2) with (without) constant term, based on the bias and RMSE criteria’s