Efficient generation of ARMA cross convariance sequences

The generation of ARMA auto and cross covariance sequences has found much interest due to its many applications. The autoregressive system part leads to purely autoregressive behavior on the tails of these sequences. Here the provision of a minimal initial set of covariances is treated, so that the recursion can be started. It turns out that this minimal order for the linear system equals the maximal autoregressive order. As it is not transparent that the associated matrix structure facilitates efficient computation, the ARMA structures are decomposed into their AR and MA cascade parts, which leads to an efficient initialization procedure using the scalar backward Levinson algorithm and FFT´S.