Minimax prediction of sequences with periodically stationary increments

Abstract

The problem of optimal estimation of linear functionals constructed from unobserved values of a stochastic sequence with periodically stationary increments based on its observations at points $ k<0$ 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 favourable spectral densities and minimax (robust) spectral characteristics of the optimal linear estimates of functionals are derived in the case where spectral densities of the sequence are not exactly known while some sets of admissible spectral densities are given.