A numerical comparison of non-linear with linear prediction for the transformed Ornstein-Uhlenbeck process
For a class of stationary processes which are defined by polynomial functions of the Ornstein-Uhlenbeck process we investigate what advantages can be expected in passing from optimal linear prediction to non-linear prediction. By "optimal" we mean the square error of prediction to be minimized. Using the SUMT algorithm as well as the VF02AD program of the Harwell Subroutine Library we computed the maximum relative error difference between both kinds of prediction. It turned out that it may be possible to achieve an improvement of up to 20% by using the best non-linear predictor.
KeywordsCovariance Function Linear Prediction Hermite Polynomial Maximum Relative Error Error Improvement
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