EXTRAPOLATION OF PERIODICALLY CORRELATED STOCHASTIC PROCESSES OBSERVED WITH NOISE

The problem of optimal linear estimation of the functional A zeta = integral(infinity)(0) a(t)zeta(t)dt depending on the unknown values of periodically correlated stochastic process zeta(t) from observations of the process zeta(t) for t < 0, where theta(t) is uncorrelated with zeta(t) periodically correlated process, is considered. Formulas for calculating the spectral characteristic and the mean square error of the optimal linear estimation of the functional are proposed in the case of spectral certainty where spectral densities are exactly known. Formulas that determine the least favorable spectral densities and the minimax (robust) spectral characteristics of optimal estimates of functionals are proposed in the case of spectral uncertainty where spectral densities are not exactly known but sets of admissible spectral densities are given.