Efficient generation of covariance sequences of multiple ARMA processes

An efficient procedure for computing autocovariance sequences of multiple autoregressive moving-average processes is proposed. While the computational complexity of existing algorithms is proportional to p ³, where p denotes the degree of the autoregressive polynomial, the procedure proposed has a complexity of O( p²). The resulting scheme leads to substantial computational savings, especially when dealing with processes with autoregressive polynomials of high degree and therefore facilitates the estimation of multiple autoregressive moving-average processes with exact maximum-likelihood methods