On the inverse of the autocovariance matrix for a general moving average process

Abstract

SUMMARY In this paper we show how the inverse for the general k th autocovariance matrix, for any r th order moving average process, can be obtained by a method which requires inverting no matrix larger than r × r . The method depends on knowing that the inverse of a certain approximating matrix ia just the k th autocovariance matrix for an r th order autoregressive process; and this result is first established. Then, generalizing an approach by Prabhakar Murthy, this inverse is then adjusted to give the required exact inverse, the appropriate algorithm being quoted. Finally, we note that, when inverting any such covariance matrix of order k , it is never necessary to invert matrices larger than [ 1 2 k ] × [ 1 2 k ] .