Linear Model With AR(1) Errors

The purpose of this paper is to study some statistical inference of linear models with AR(1) errors, which have extensive applications in many fields, in particular, such as economics, management and engineering. For these models, an approach for statistical inference is to ignore the existence of error correlation and then to apply standard least squares method under Gauss-Markov assumption, this will cause some series problems in parameter estimation and hypothesis test in many cases. Thus study of these models has obtained a great attention of statisticians for a long period.In this paper we propose a new estimate of variance parameter and discuss its some statistical properties. Our simulation results show that for high errors correlation case, new estimate is superior over the moment estimate appeared in literature under mean square error criterion. However, two-stage estimates of regression coefficients corresponding to these two estimates have approximate equal mean square error.For testing linear hypothesis about regression coefficients, Banerjee and Magnus(1997) studied the sensitivity of F-test sta,tistic(FGLS( )) based on generalized least square estimate caused by variance parameter in general case and proposed sensitivity statistic and its distribution. In this paper two new test statistics by using matching the first three moments approach are proposedto approximate FGLS( ) by x2 and F variables. A comparison with modified F-test by Wu et al (1988) is completed. Our simulation results show that for high positive errors correlation cases, these new tests have lower type-1 error and large power than modified F-test.