ON THE PECULIARITIES OF USING POLYNOMIAL PREDICTION SEQUENCES IN INTELLIGENT DATA ANALYSIS ALGORITHMS UNDER CONVERGENCE CONDITIONS

Abstract

The paper investigates the specific features of using sequences of polynomial predictions (PPS) in intelligent data analysis algorithms under convergence conditions. The relevance of the study is determined by the need to construct efficient short-term forecasts under limited data availability and in the absence of an adequate a priori mathematical model of the underlying process. In contrast to traditional approaches based on a single fixed-degree polynomial, the proposed method relies on analyzing a sequence of one-step polynomial predictions and studying their convergence to an unknown forecast value.

Strict conditions for the convergence of polynomial prediction sequences are obtained and proven in the classical case when a function is given at a countable set of uniformly spaced grid points. For the practically important case of finite time series, an analogue of the convergence concept is introduced, and a forecasting method based on the intelligent analysis of PPS structure is developed. The notions of binomially stable functions, conditionally binomially stable functions, and binomially stable data are introduced. The non-emptiness of the corresponding function classes is justified, and representative examples are provided. It is shown that for conditionally binomially stable functions, the convergence of PPS depends on the grid step size; sufficient conditions on the discretization step ensuring convergence for certain function classes are established.

Numerical experiments confirm the theoretical findings and demonstrate the high accuracy of the proposed approach. An algorithm for detecting coincidences within the PPS set is proposed and shown to be effective even for short sequences. The obtained results indicate the перспективність of applying polynomial prediction sequences in intelligent data analysis tasks and provide a foundation for further research aimed at improving noise robustness and generalizing convergence conditions.