Open AccessRobust Filtering of Sequences with Periodically Stationary Multiplicative Seasonal Increments
Author(s) -
Maksym Luz,
Mikhail Moklyachuk
Publication year - 2021
Publication title -
statistics, optimization and information computing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.297
H-Index - 12
eISSN - 2311-004X
pISSN - 2310-5070
DOI - 10.19139/soic-2310-5070-1197
Subject(s) - mathematics , cyclostationary process , stationary sequence , sequence (biology) , multiplicative function , minimax , stationary process , semimartingale , spectral density , stochastic process , mathematical optimization , mathematical analysis , statistics , computer science , computer network , channel (broadcasting) , biology , genetics
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.