| The time series regression model was widely studied in the literature by several authors. However, statistical analysis of replicated time series regression models has received little attention. In this thesis, we study the application of quasi-least squares, a relatively new method, to estimate the parameters in replicated time series models with general ARMA( p, q) correlation structure. We also study several established methods for estimating the parameters in those models, including the maximum likelihood, method of moments, and the GEE method. Asymptotic comparisons of the methods are made bV fixing the number of repeated measurements in each series, and letting the number of replications n go to infinity. Our theoretical as well as some simulation results show that the quasi-least squares estimates are undoubtedly better than the moment estimates, and are good competitors and more robust than the maximum likelihood estimates. Examples are presented to illustrate the application of the quasi-least squares method to analyze real life data situations. |
