Interpolation of periodically correlated stochastic sequences

Abstract

We study the problem of optimal estimation of a linear functional of unknown values of a periodically correlated random sequence from observed values of a sequence with an additive noise. Formulas for calculating the mean square error and spectral characteristic of the optimal linear estimate of a functional are established in the case where the spectral densities are known. The least favorable spectral densities and minimax spectral characteristic of the optimal linear estimate of a functional are found for some classes of admissible spectral densities.