Luz M. Estimates of functionals from processes with stationary increments

Formulas which allow to calculate spectral characteristics and the values of mean square errors of the optimal estimates of the linear functionals of unknown values of the stochastic sequences and processes with stationary increments are proposed provided certainty of the spectral structure of the sequences and the processes. Formulas for calculating spectral characteristics and the values of mean square errors of the optimal estimates of the linear functionals of a class of cointegrated sequences are derived for the filtering problem. The problems of minimax-robust interpolation, extrapolation and filtering of the functionals of unknown values of the stochastic sequences and processes with stationary increments are stated and solutions to these problems are proposed, namely, formulas and relations that allow to find the least favorable spectral densities and the minimax-robust spectral characteristics are derived.