Computation of cumulants of ARMA processes

Using the observable state-space realization corresponding to a given multi-input-multi-output autoregressive moving average (ARMA) model, the authors derive closed-form and lag-recursive expressions for the cumulants of the output process. Their approach involves the computation of cumulants of vector processes, which they define compactly in terms of Kronecker products, and leads to a unified treatment of multichannel, time-varying and nonstationary processes. Computational aspects are discussed in detail. A new cumulant-based identification method is proposed in which the matrices of the SSM are first estimated and then transformed to ARMA parameters