On the problem of filtration for vector stationary sequences

We study the problem of optimal linear estimation of the functional $A\vec \xi =\sum _{j=0}^\infty {\vec a(j)\vec \xi ( - j)}$ depending on unknown values of a vector stationary sequence $\vec \xi (j)=\{\xi _k(j)\}_{k=1}^T$ from observations upon the sequence $\vec \xi (j)+\vec \eta (j)$ for $j \leq 0$ where $\vec \eta (j)=\{\eta _k(j)\}_{k=1}^T$ is a vector stationary sequence, being uncorrelated with $\vec \xi (j)$. We obtain relations for the mean square error and spectral characteristic of the optimal estimator of the functional. We also find the least favorable spectral densities and minimax (robust) spectral characteristics of optimal estimators of the functional for a particular class $D$ of spectral densities.