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Biometrika 1976 63(2):391-394; doi:10.1093/biomet/63.2.391
© 1976 by Biometrika Trust
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On the inverse of the autocovariance matrix for a general moving average process

O. D. ANDERSON

Civil Service College London

In this paper we show how the inverse for the general kth autocovariance matrix, for any rth 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 kth autocovariance matrix for an rth 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 .

Key Words: Autocovariance matrix • Autoregreesive process; • Moving average process


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