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

Maksym Luz; Mikhail Moklyachuk

doi:10.19139/soic-2310-5070-1408

Maksym Luz BNP Paribas Cardif, Kyiv, Ukraine https://orcid.org/0000-0002-8260-1584
Mikhail Moklyachuk Kyiv National Taras Shevchenko University, Ukraine

DOI: https://doi.org/10.19139/soic-2310-5070-1408

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

Abstract

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.

Author Biography

Mikhail Moklyachuk, Kyiv National Taras Shevchenko University, Ukraine

Department of Probability Theory, Statistics and Actuarial Mathematics, Professor

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