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Abstract. The topic of serial correlation in regression models has attracted a great deal of research in the last fifty years. Most of these studies have assumed that the structure of the error covariance matrix was known or could be consistently estimated from the data. In this article we describe a new procedure for generating forecasts for regression models with serial correlation based on ordinary least squares and on an approximate representation of the form of the autocorrelation. We prove that the predictors from this specification are asymtotically efficient under some regularity conditions. In addition we show that there is not much to be gained in trying to identify the correct form of the serial correlation since efficient forecasts can be generated using autoregressive approximations of the autocorrelation. A large simulation study is also used to compare the finite sample predictive efficiencies of this new estimator vis-`a-vis estimators based on ordinary least squares and generalized least squares.
Keywords: Autocorrelation; Autoregressive Moving Average; Least Squares; Model Identification; Prediction.