Method of an optimal nonlinear extrapolation of a noisy random sequence on the basis of the apparatus of canonical expansions

Abstract

Method of optimal nonlinear extrapolation of a random sequence provided that the measurements are carried out with an error is developed using the apparatus of canonical expansions. Filter-extrapolator does not impose any essential limitations on the class of predictable random sequences (linearity, Markovian behavior, stationarity, monotony etc.) that allows to achieve maximum accuracy of the solution of a prediction problem. The results of a numerical experiment on a computer confirmed high effectiveness of the introduced method of the prediction of the realizations of random sequences. Expression for a mean-square error of extrapolation allows to estimate the quality of a prediction problem solving using a developed method. The method can be used in different spheres of science and technics for the prediction of the parameters of stochastic objects.