Extrapolation Problem for Stochastic Sequences with Stationary n th Increments Based on Observations with Stationary Noise
Maksym Luz, Mikhail Moklyachuk · 2019
This chapter presents the results of the investigation of the extrapolation problem of mean-square optimal linear estimation of the functionals Aξ and ANξ, which depend on the unobserved values ξ(m) of the stochastic sequence ξ(m) with stationary increments of order n. As a noise sequence, it considers a stationary sequence ξ(m) which is uncorrelated with the sequence ξ(m). In the case of spectral uncertainty where the spectral densities are not known exactly while a set of admissible spectral densities is given, the minimax method of estimation of the functionals which depends on the unobserved values of stochastic sequences with stationary increments is applied. For more detailed analysis of properties of the least favorable spectral densities and the minimax–robust spectral characteristics, the minimax spectral characteristic and the pair of the least favorable spectral densities form a saddle point.