The Study Of Linear Regression Model With AR(2) Errors

Based on studying some statistical inference of linear models with AR(1) errors, the purpose of this statistical inference of linear models with AR(2) errors. This kind of models has extensive applications in many fields, in particular, such as economics, management, engineering, forestry and ecology. 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 test, 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.For parameter estimation of linear models with AR(2) errors, the paper obtains the covariance matrix of the error vector and its inverse matrix and obtains transformation matrix of weighted 2-order differences, based on studying linear models with AR(1) errors. Then estimates parameters of linear models with AR(2) errors with the cycle generalized least squares (CGLS). Under mean square error criterion, Simulation results show that efficiency of CGLS method is superior over the method of two steps generalized least squares (GLS). Furthermore the paper studies errors parameters with some special relationship in linear regression model with AR(2) errors. The result shows considering the special relationship is superior over notIn this paper we propose a new estimate, Distance Partial correlation coefficient iteration estimation of variance parameter, which takes defect of the moment estimation (only with adjacent variable information). Simulation results show that for high errors correlation case and high order errors correlation case, new estimate is superior over the moment estimate and the CO iteration estimate appeared in literature under mean square error criterion.The paper also discusses autocorrelation test of the linear regression model and studies some methods of autocorrelation test of the linear regression model with high order autocorrelation errors, and explains treatment process of the linear regression model with high order autocorrelation errors with examples.