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).
Publié le : 1984-05-14
Classification:
$q$-variate stationary processes,
Fourier series and coefficients,
linear interpolation,
interpolator,
minimality,
angle,
spectral density function,
62M10,
60G12
@article{1176993308,
author = {Pourahmadi, Mohsen},
title = {On the Mean Convergence of the Best Linear Interpolator of Multivariate Stationary Stochastic Processes},
journal = {Ann. Probab.},
volume = {12},
number = {4},
year = {1984},
pages = { 609-614},
language = {en},
url = {http://dml.mathdoc.fr/item/1176993308}
}
Pourahmadi, Mohsen. On the Mean Convergence of the Best Linear Interpolator of Multivariate Stationary Stochastic Processes. Ann. Probab., Tome 12 (1984) no. 4, pp. 609-614. http://gdmltest.u-ga.fr/item/1176993308/