On the closed form of the covariance matrix and its inverse of the causal ARMA process

John N. Haddad

Journal of Time Series Analysis, 2004, vol. 25, issue 4, 443-448

Abstract: Abstract. Derivation of the theoretical autocovariance function of a causal autoregressive moving‐average process of order (p, q), ARMA(p, q), when q ≥ 1 is considered. A recursive relationship is established between the covariance matrices of an ARMA(p, q) process and its associated ARMA(p, q−1) process. The obtained recursion is shown to produce the inverse of the covariance matrix and its determinant. Moreover, the introduced method can be easily implemented in any programming environment.

Date: 2004
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https://doi.org/10.1111/j.1467-9892.2004.01454.x

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