Estimation of the Trend Model with Autoregressive Errors

A popular model for assessing dependence on time is the linear trend plus autoregressive error model. Considerable effort has been devoted toward efficient esitmation of and testing for a linear trend in the presence of serial correlation. However, the testing procedures used in practice do not perform satisfactorily over the whole parameter range because the variance of the feasible generalized least squares estimator of the trend coefficient is heavily dependent on the parameters of the autoregressive process. We develop estimators of the variance of the estimated trend coefficient that form the basis for tests that perform relatively well over the whole range of parameters for the autoregressive process. Limiting distributions are derived for the proposed test statistics.