Specification Analysis

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Abstract
A spectral-theoretic approach is taken to derive general results concerning the effect on mean square prediction error of any misspecification of the linear model describing a real-valued stochastic process in discrete time. Attention is restricted to the important case of one-step ahead prediction and the class of autoregressive integrated moving averages of order (p,d,q). It is shown that the problem of calculating any predictor's relative efficiency, defined as the ratio of the minimum achievable mean square error to the actual mean square error, can always be reduced to the problem of evaluating a definite integral of particularly simple form. Examples of the usefulness of these results for applied time series analysis and forecasting are given.

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