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On the closed form of the covariance matrix and its inverse of the causal ARMA process
Author(s) -
Haddad John N.
Publication year - 2004
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.2004.01454.x
Subject(s) - autocovariance , mathematics , recursion (computer science) , autoregressive–moving average model , covariance function , covariance , autoregressive model , inverse , covariance matrix , estimation of covariance matrices , matérn covariance function , matrix (chemical analysis) , rational quadratic covariance function , moving average , statistics , covariance intersection , algorithm , mathematical analysis , fourier transform , geometry , composite material , materials science
. 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.