Minimax-robust forecasting of sequences with periodically stationary long memory multiple seasonal increments

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


We introduce a stochastic sequence $\zeta(k)$ with periodically stationary generalized multiple increments of fractional order which combines cyclostationary, multi-seasonal, integrated and fractionally integrated patterns. We solve the problem of optimal estimation of linear functionals constructed from unobserved values of the stochastic sequence $\zeta(k)$  based on its  observations at points $ k<0$. 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 estimates of the functionals. Formulas that determine the least favorable spectral densities and minimax (robust) spectral characteristics of the optimal linear estimates 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. (2020). Minimax-robust forecasting of sequences with periodically stationary long memory multiple seasonal increments. Statistics, Optimization & Information Computing, 8(3), 684-721.
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