Abstract
It is shown that a necessary and sufficient condition, for the existence of a mean-convergent series for the linear interpolator of a $q$-variate stationary stochastic process $\{X_n\}$ with density matrix $W$, is that the Fourier series of the isomorph of the linear interpolator should converge in the norm of $L^2(W)$, and this happens if the past and future of the process are at positive angle. This provides a positive answer to a question of H. Salehi (1979) concerning the square summability of the inverse of $W$ and improves upon the work of Rozanov (1960) and Salehi (1979).
Citation
Mohsen Pourahmadi. "On the Mean Convergence of the Best Linear Interpolator of Multivariate Stationary Stochastic Processes." Ann. Probab. 12 (2) 609 - 614, May, 1984. https://doi.org/10.1214/aop/1176993308
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