The Algorithm of Optimal Polynomial Extrapolation of Random Processes

Abstract

This work deals with the modelling and prediction of the realizations of random processes in corresponding future time moments. The extrapolation algorithm of nonlinear random process for arbitrary quantity of known significances and random relations used for forecasting has been received on the basis of mathematical instrument of canonical decomposition. The received optimal solutions of the nonlinear extrapolation problem, as well as the canonical decomposition, that was use as a base for optimal solution, does not set any substantional restrictions on the class of investigated random process (liniarity, Markov processes propety, stationarity, monotonicity etc.). Theoretical results, block-diagrams for calculation procedures and the analysis of applied applications, especially for the prediction of economic indexes and parameters of technical devices, are under discussions.