Date of Award
Doctor of Philosophy
Estimation of the parameters of the stationary normal seasonal autoregressive process with seasonal means is studied. For samples of the size frequently encountered in econometrics, the least squares estimators of the autoregressive coefficients are seriously biased. Alternative estimators are studied;Using large sample theory, approximations to the first two moments of the seasonal autoregressive parameter are derived. The bias expression is used to develop modifications of the least squares estimator with smaller bias for most values of (rho). Although the least squares estimator and the proposed modifications are asymptotically equivalent, the small sample behavior of the two estimators is considerably different;The asymptotic biases of the least squares estimators of the stationary normal second-order seasonal autoregressive parameters are derived. Three bias correction procedures which remove the bias due to the estimation of means are proposed. These procedures are considerably more complex than those developed for the first-order process. The methods of bias correction can be extended to higher order processes;A large Monte Carlo study examining the small sample properties of the various estimators of the first-order seasonal autoregressive parameter and of associated predictors is presented. The Monte Carlo study demonstrates that approximating the null distributions of the regression "t-statistics" by the Student's t distribution is not appropriate for the ordinary least squares estimator in small samples. The empirical distribution of the "t-statistic" for the modified estimators was much closer to the tabled distribution. Generally speaking, the predictors constructed from the modified estimator performed better than the least squares predictor;Examples of seasonal autoregressive processes for which the above results are applicable are presented.
Digital Repository @ Iowa State University, http://lib.dr.iastate.edu/
Edward Henry Lee
Lee, Edward Henry, "Estimation of seasonal autoregressive time series " (1981). Retrospective Theses and Dissertations. 7442.