On the problem of filtration of vector stationary sequences. (Ukrainian, English) Zbl 1164.60358

Moklyachuk, M. P.; Masyutka, O. Yu.

Teor. Jmovirn. Mat. Stat. 75, 95-104 (2006); translation in Theory Probab. Math. Stat. 75, 109-119 (2007).

The authors study the problem of optimal linear estimation of the functional \(A\vec\xi=\sum_{j=0}^{\infty}\vec a(j)\vec\xi(-j)\) for unknown values of the stationary vector sequence \(\vec\xi(j)=\{\xi_{k}(j)\}_{k=1}^{T}\), with spectral density \(F(\lambda)\), on the basis of observations of the sequence \(\vec\xi(j)+\vec\eta(j)\), as \(j\leq0\), where \(\vec\eta(j)\) is a stationary vector sequence with spectral density \(G(\lambda)\) which is uncorrelated with \(\vec\xi(j)\). Formulas are derived for the calculation of the mean square error and the spectral characteristic of the optimal estimate of the functional. The authors find the least favourable spectral characteristics of the optimal estimates of the functional for a fixed class of spectral densities.

Reviewer: Aleksandr D. Borisenko (Kyïv)

MSC:

60G35	Signal detection and filtering (aspects of stochastic processes)
62M20	Inference from stochastic processes and prediction

Keywords:

filtration; vector stationary sequences; optimal linear estimation; spectral density