On the Closed Form of the Covariance Matrix and its Inverse of the Causal Arma Process

Derivation of the theoretical autocovariance function of a causal autoregressive moving-average process of order (p,q), ARMA(p,q), when q greater than or equal to 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