The method of optimal nonlinear extrapolation of vector random sequences on the basis of polynomial degree canonical expansion

Abstract

The given work is dedicated to the solving of important scientific and technical problem of forming of the method of the optimal (in mean-square sense) extrapolation of the realizations of vector random sequences for the accidental quantity of the known values used for prognosis and for various order of nonlinear stochastic relations. Prognostic model is synthesized on the basis of polynomial degree canonical expansion of vector random sequence. The formula for the determination of the mean-square error of the extrapolation which allows us to estimate the accuracy of the solving of the prognostication problem with the help of the introduced method is obtained. The block diagrams of the algorithms of the determination of the parameters of the introduced method are also presented in the work. Taking into account the recurrent character of the processes of the estimation of the future values of the investigated sequence the method is quite simple in calculating respect. The introduced method of extrapolation as well as the vector canonical expansion assumed as its basis doesn’t put any essential limitations on the class of prognosticated random sequences (linearity, Markovian property, stationarity, scalarity, monotony etc.).