A unified approach to modeling multichannel ARMA processes

Using a compact Kronecker-product-based representation for the cumulants of vector processes, the authors develop several techniques for estimating the parameters of a multichannel ARMA (autoregressive moving average) process, from sample cumulants of the output processes: (1) the AR parameters are estimated first; the MA parameters are then estimated from the AR compensated time series. (2) AR and IR (impulse response) parameters are estimated simultaneously; (3) an algorithm that handles causal as well as noncausal ARMA models, by transforming the ARMA parameter estimation problem to a pair of MA parameter estimation problems, is given. Order-determination techniques are also proposed. The algorithms are applicable to both stochastic and deterministic problems