Convenient Methods for Estimation of Linear Regression Models with MA(1) Errors

This paper proposes computationally convenient methods for estimating linear regression models with first-order moving average, or MA(1), error structures. Conditional on alpha, the parameter of the MA(1) process, estimates of the regression coefficients may be obtained by ordinary least squares. Searching over alpha then yields full maximum likelihood estimates. A method of moments estimator for alpha can also be used to obtain less efficient but computationally simpler estimates. The performance of these two estimators is investigated by sampling experiments. An empirical example is presented involving the relationship between GNP and unemployment.