Thesis (Ph.D.) - Cairo University - Institute of Statistical Studies and Research - Department of Statistics and Econometrics

In this Thesis, some useful lemmas are derived to prove the limiting distributions of the least squares estimators for AR(1) model with time trend in unit root and stationary cases. The time variable was included in the model in two ways: As main e{uFB00}ect or interaction e{uFB00}ect. The limiting distributions of least squares estimators and their corresponding standardized form for AR (1) model with time trend are derived under the null hypothesis that the true model is random walk with (without) constant term or with (without) time trend term. Also, the limiting distributions of the least squares estimators for stationary AR(1) model with polynomial time trend are derived under the null hypothesis that the true model is AR (1) with (without) constant term or is a white noise. A statistical analysis for these estimates in unit root case is conducted by using simulation experiments at 25000 replicates for di{uFB00}erent sample size to show whether the distribution is stable or not, with change in sample size. The critical values of these simulated estimates are computed for di{uFB00}erent sample size and di{uFB00}erent signi{uFB01}cance levels to be used in statistical inference. A real data is used to illustrate the application of AR(1) model with time trend to {uFB01}t mortality rates in life insurance companies

Issued also as CD