Estimation of Parameters in Time-Series Regression Models

Summary We consider the estimation of the coefficients in a general linear regression model in which some of the explanatory variables are lagged values of the dependent variable. For discussing optimum properties the concept of best unbiased linear estimating equations is developed. It is shown that when the errors are normally distributed the method of least squares leads to optimum estimates. The properties of the least-squares estimates are shown to be the same asymptotically as those of the least-squares coefficients of ordinary regression models containing no lagged variables, whether or not the errors are normally distributed. Finally, a method of estimation is proposed for a different model which has no lagged dependent variables but in which the errors have an autoregressive structure. The method is shown to be efficient in large samples.