Robust Forecasting of Sequences with Periodically Stationary Long Memory Multiplicative Seasonal Increments Observed with Noise and Cointegrated Sequences

Fuente: arXiv
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Main Authors: Luz, Maksym, Moklyachuk, Mykhailo
Format: Preprint
Published: 2025
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author Luz, Maksym
Moklyachuk, Mykhailo
author_facet Luz, Maksym
Moklyachuk, Mykhailo
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2511_04905
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Robust Forecasting of Sequences with Periodically Stationary Long Memory Multiplicative Seasonal Increments Observed with Noise and Cointegrated Sequences
Luz, Maksym
Moklyachuk, Mykhailo
Statistics Theory
60G10, 60G25, 60G35, 62M20, 93E10
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.
title Robust Forecasting of Sequences with Periodically Stationary Long Memory Multiplicative Seasonal Increments Observed with Noise and Cointegrated Sequences
topic Statistics Theory
60G10, 60G25, 60G35, 62M20, 93E10
url https://arxiv.org/abs/2511.04905