THE INVERSE OF COVARIANCE MATRICES FOR THE ARMA (p, q) CLASS OF PROCESSES

Document Type: Regular Paper

Authors

1 Department of Statistics, University of Shahid Chamran, Ahvaz, I. R. of Iran

2 Unilever Research Port Sunlight, Quarry Road East, Bebington, Wirral, CH633JW, UK

Abstract

Analysis of time series data can involve the inversion of large covariance matrices. For the
class of ARMA (p, q) processes there are no exact explicit expressions for these inverses, except for the
MA (1) process. In practice, the sample covariance matrix can be very large and inversion can be
computationally time consuming and so approximate explicit expressions for the inverse are desirable.
This paper offers some of these approximations.

Keywords