Robust extrapolation problem for stochastic sequences with stationary increments

2025/10/19 by Maksym Luz, Luz, Maksym, Moklyachuk, Mykhailo · 1 citation
Mathematics · Economics, Econometrics and Finance · #Mathematical Approximation and Integration #Stochastic processes and financial applications #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.2510.16900

Abstract

The problem of optimal estimation of functionals Aξ=∑\nolimits_k=0^∞ a(k)ξ(k) and A_Nξ=∑\nolimits_k=0^Na(k)ξ(k) which depend on the unknown values of stochastic sequence ξ(k) with stationary nth increments is considered. Estimates are based on observations of the sequence ξ(m) at points of time m=-1,-2,…. Formulas for calculating the value of the mean square error and the spectral characteristic of the optimal linear estimates of the functionals are derived in the case where spectral density of the sequence is exactly known. Formulas that determine the least favorable spectral densities and minimax (robust) spectral characteristic of the optimal linear estimates of the functionals are proposed in the case where the spectral density of the sequence is not known but a set of admissible spectral densities is given.

Citations

• On Minimax Estimation Problems for Periodically Correlated Stochastic Processes

Cited by

• On Minimax Estimation Problems for Periodically Correlated Stochastic Processes

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