Robust Filtering of Sequences with Periodically Stationary Multiplicative Seasonal Increments

Keywords: Periodically stationary sequence, SARFIMA, fractional integration, filtering, optimal linear estimate, mean square error, least favourable spectral density matrix, minimax spectral characteristic


We consider stochastic sequences with periodically stationary generalized multiple increments of fractional order which combines cyclostationary, multi-seasonal, integrated and fractionally integrated patterns. We solve the filtering problem for linear functionals constructed from unobserved values of a stochastic sequence of this type based on observations of the sequence with a periodically stationary noise sequence. For sequences with known matrices of spectral densities, we obtain formulas for calculating values of the mean square errors and the spectral characteristics of the optimal filtering of the functionals. Formulas that determine the least favourable spectral densities and the minimax (robust) spectral characteristics of the optimal linear filtering of the functionals are proposed in the case where spectral densities of the sequence are not exactly known while some sets of admissible spectral densities are given.

Author Biography

Mikhail Moklyachuk, Kyiv National Taras Shevchenko University
Department of Probability Theory, Statistics and Actuarial Mathematics, Professor


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How to Cite
Luz, M., & Moklyachuk, M. (2021). Robust Filtering of Sequences with Periodically Stationary Multiplicative Seasonal Increments. Statistics, Optimization & Information Computing, 9(4), 1010-1030.
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