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

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  • John N. Haddad

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.

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  • John N. Haddad, 2004. "On the closed form of the covariance matrix and its inverse of the causal ARMA process," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(4), pages 443-448, July.
    • Handle: RePEc:bla:jtsera:v:25:y:2004:i:4:p:443-448
    DOI: 10.1111/j.1467-9892.2004.01454.x
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    References listed on IDEAS

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    1. Anderson, T. W. & Mentz, Raúl P., 1977. "The generalized variance of a stationary autoregressive process," Journal of Multivariate Analysis, Elsevier, vol. 7(4), pages 584-588, December.
    2. van der Leeuw, Jan, 1994. "The covariance matrix of ARMA errors in closed form," Journal of Econometrics, Elsevier, vol. 63(2), pages 397-405, August.
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    Cited by:

    1. Serge B. Provost & John N. Haddad, 2019. "A recursive approach for determining matrix inverses as applied to causal time series processes," METRON, Springer;Sapienza Università di Roma, vol. 77(1), pages 53-62, April.

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