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Volume 58 >>> № 1 JANUARY — FEBRUARY 2022

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UDC 519.21

M.M. Luz¹, M.P. Moklyachuk²

¹ BNP Paribas Cardif, Ukraine

maksim_luz@ukr.net

² Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

moklyachuk@gmail.com

MINIMAX FILTERING OF SEQUENCES WITH PERIODICALLY STATIONARY INCREMENTS

Abstract. The authors consider the problem of optimal filtering of linear functionals that depend on unknown values of the stochastic sequence with periodically stationary increments based on observations of the sequence with a stationary noise. For sequences with known spectral densities, formulas for the values of the root-mean-square errors and spectral characteristics of the optimal estimates of the functionals are obtained. Formulas that determine the least favorable spectral densities and minimax (robust) spectral characteristics of the optimal linear estimates of functionals are proposed in the case where spectral densities of the sequence are not known exactly while some sets of feasible spectral densities are given.

Keywords: periodically stationary increments, minimax-robust estimate, least favorable spectral density.

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