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Baltagi and Li (1991) give a transformation which may be applied to certain autocorrelated disturbances in an error-components model to yield spherical disturbances. They derive the transformation for AR(1) and AR(2) cases. We show that the results of Galbraith and Zinde-Walsh (1992) on the general ARMA form of the transformation matrix can be applied to allow estimation of the error-components model with disturbances which follow any ARMA (p, q) process. We also show that, for models with a cross-sectional dimension which is large relative to the time dimension, it is possible to use this method to perform a general autocorrelation transformation without specifying a particular ARMA process or estimating ARMA parameters.Key words: ARMA process; Autocorrelation; Error-components model JEL classification: 211

It is well known that consistent estimation of a linear regression model with a stationary Gaussian ARMA process in the errors can be carried out by maximum likelihood or, alternatively, by two-stage procedures involving estimation of the nuisance parameters followed by feasible generalized least squares for the model parameters. We show that the estimators coincide up to [O.sub.p]([T.sup.-3/2]) and derive the variance to O([T.sup.-2]), which up to terms of this order is the same for both estimators. Considering the form of the error covariance matrix for an ARMA (p, q) process allows us to examine a computationally convenient algorithm for estimation of the parameters of the regression model. Finally we provide a Monte Carlo comparison of the small-sample properties of OLS and two versions of the proposed estimator.

This paper considers the distributions of augmented Dickey-Fuller statistics to test for a unit root in the presence of errors that have a moving average part. We examine the dependence of the augmented Dickey-Fuller statistic on the order, k, of the approximating autoregression, by deriving the asymptotic distribution of the statistic for finite k. The results provide a direct indication of the rate of growth of k with sample size that is necessary in order to avoid non-negligible size distortions, and are illustrated by simulations that provide empirical densities for various cases of interest. The size distortions are particularly difficult to control when the moving average part contains a root near unity; for such cases we examine the distribution of the ADF statistics in models estimated by feasible GLS, rather than OLS, to control for the moving-average component. We find that both size distortions and sensitivity of the test statistic to k are greatly reduced in this case. Keywords: Augmented Dickey-Fuller test; Moving-average process; Unit root