Least squares estimation in the regression model with autoregressive-moving average errors

SUMMARY To treat the problem of correlated errors in regression, a model in which the errors follow a stationary autoregressive-moving average time series is suggested. Simultaneous least squares estimation of the regression and the time series parameters is discussed, and it is shown that asymptotically the estimates obtained in this manner possess normal distributions, whether or not the errors themselves are normally distributed. The estimates of the regression parameters are uncorrelated with those of the time series parameters; the former are distributed as if they had arisen from a certain transformed model with uncorrelated errors, while the latter have the same covariance matrix as those from a stationary series with no deterministic component. The estimate of variance is also asymptotically normal. A Monte Carlo sampling study indicates that these results can serve as a useful approximation for samples of moderate size.