Abstract.Using both the maximum likelihood estimator and the Bayes estimator, we consider estimating the regression model with the first-order autocorrelated error, where the initial distribution of the autocorrelated error is taken into account. For the Bayes estimator, the Gibbs sampler and the Metropolis-Hastings algorithm are utilized to obtain random draws of the parameters. As a result, the Bayes estimator is less biased and more efficient than the maximum likelihood estimator. Especially, for the autocorrelation coefficient, the Bayes estimate is much less biased than the maximum likelihood estimate. Accordingly, for the standard error of the estimated regression coefficient, the Bayes estimate is more plausible than the maximum likelihood estimate, because variance of the estimated regression coefficient depends on the estimated autocorrelation coefficient. Thus, we find that the Bayes approach might be recommended in the empirical studies.

Received: February 4, 2003

AMS Subject Classification: 62M10, 62F15

Key Words and Phrases: autoregressive model, Gibbs sampler, Metropolis-Hastings algorithm, Bayes estimator, MLE

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2003
Volume: 5
Issue: 2