An application of the theory of equivalence of Gaussian measures to a prediction problem

An extension of a general theorem by J.A. Bucklew (ibid., vol. IT-31, 677-679, 1985) on the asymptotic optimality of a linear predictor based on an incorrect covariance function is given. The result is applied to the problem of predicting a small time lag into the future to obtain an easily verifiable condition under which the Taylor series predictor given by Bucklew is nearly optimal. The critical condition of the theorem is as follows: Gaussian measures corresponding to the covariance function used to obtain the predictors and the actual covariance function must be equivalent probability measures (i.e., mutually absolutely continuous measures)