Abstract
The mathematical theory of the best linear prediction of stationary time series presumes that the model generating the series, which can be specified by either the autocovariance function or the spectral density, is known. The true model is, of course, not known in practice, and the procedure is to fit a model and predict as if this fitted model were the truth. The question then is one of deciding whether the resulting predictions are about as good as could be gotten if the truth were known. This paper describes a method for assessing the predictions of the fitting model by an analysis of residuals. In particular, it is argued that the traditional tests of hypothesis for white noise are inappropriate if prediction is the goal, and a method is described for determining whether or not the mean square errors of the predictions arising from the fitted model can be measurably reduced.
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