Open AccessRobust Forecasting of Sequences with Periodically Stationary Long Memory Multiplicative Seasonal Increments Observed with Noise and Cointegrated Sequences
Author(s) -
Maksym Luz,
Mikhail Moklyachuk
Publication year - 2022
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-2310-5070-1408
Subject(s) - mathematics , sequence (biology) , multiplicative function , minimax , noise (video) , stationary sequence , spectral density , spectral density estimation , spectral analysis , stationary process , spectral slope , multiplicative noise , statistical physics , stochastic process , spectral line , mathematical analysis , statistics , mathematical optimization , computer science , physics , fourier transform , signal transfer function , artificial intelligence , spectroscopy , analog signal , image (mathematics) , genetics , biology , quantum mechanics , digital signal processing , astronomy , computer hardware
The problem of optimal estimation of linear functionals constructed from unobserved values of stochastic sequence with periodically stationary increments based on observations of the sequence with a periodically stationary noise is considered. For sequences with known spectral densities, we obtain formulas for calculating values of the mean square errors and the spectral characteristics of the optimal estimates of the functionals. 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 exactly known while some sets of admissible spectral densities are given.