COMPARISON OF SOME ORTHOGONAL FUNCTION SYSTEMS FOR KOLMOGOROV-WIENER FORECASTING OF MFSD PROCESS
DOI:
https://doi.org/10.15588/1607-3274-2026-2-1Keywords:
Kolmogorov-Wiener filter weight function, Walsh functions, telecommunication traffic, MFSD model, Bessel functions, Galerkin methodAbstract
Context. We investigate such orthogonal function systems as the Walsh function one and the Bessel function one for the search
of the weight function of the Kolmogorov-Wiener (KW) filter for the forecasting of the heavy-tail MFSD (multifractal fractional sum-difference) random process. The results for the MAPE (mean absolute percentage error) of the misalignment of both sides of the Wiener-Hopf integral equation are compared to that obtained by the Chebyshev polynomial expansion in our previous paper.
Objective. The objective is to derive the weight function of the KW continuous filter via the truncated expansions in Walsh and Bessel functions and to compare results with the results obtained via the Chebyshev polynomials in our previous paper.
Method. Galerkin method with the Walsh functions and the Bessel functions orthogonal on the required interval as the method basis is used.
Results. It is shown that the choice of Walsh functions leads to better results for the above-described MAPE than the choice of the Chebyshev polynomials and Bessel functions. It is shown that the choice of the orthogonal polynomials is more effective than the choice of the Bessel functions. It is also obtained that of the approximation of 128 Walsh functions leads to the MAPE less than 0.5%.
Conclusions. The weight function of the KW filter in the continuous case is investigated for the forecasting of a random stationary heavy-tail process in the MFSD model. The Walsh functions and Bessel functions are chosen to be the basis of the Galerkin method described in the paper. The results are compared to that obtained with the choice of the Chebyshev polynomials. It is obtained that the Walsh functions lead to the most reliable results among the above-mentioned orthogonal function systems. The calculated results may be applied for the practical forecasting of traffic in telecommunications and also they may be applied to the treatment of random processes in other fields of knowledge: in agriculture, etc.
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Copyright (c) 2026 V. N. Gorev, Y. I. Shedlovska, I. S. Laktionov, G. G. Diachenko
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