2025/10/19 by Moklyachuk, Mykhailo, Maria Sidei, Sidei, Maria
Economics, Econometrics and Finance · Environmental Science · Mathematics · #Stochastic processes and financial applications #Analysis of environmental and stochastic processes #Statistical and numerical algorithms
paper · pdf · doi:10.48550/arxiv.2510.16908
The problem of the mean-square optimal linear estimation of the functional Aξ= ∫Rsa(t)ξ(-t)dt, which depends on the unknown values of stochastic stationary process ξ(t) from observations of the process ξ(t)+η(t) at points t∈ℝ - \backslash S , S=\bigcupl=1s[-Ml-Nl, …, -Ml ], Rs=[0,∞) \backslash S+, S+=\bigcupl=1s[ Ml, …, Ml+Nl] is considered. Formulas for calculating the mean-square error and the spectral characteristic of the optimal linear estimate of the functional are proposed under the condition of spectral certainty, where spectral densities of the processes ξ(t) and η(t) are exactly known. The minimax (robust) method of estimation is applied in the case where spectral densities are not known exactly, but sets of admissible spectral densities are given. Formulas that determine the least favorable spectral densities and the minimax spectral characteristics are proposed for some special sets of admissible spectral densities.