Multichannel ARMA processes

Parametric modeling of multichannel time series is accomplished by using higher (than second) order statistics (HOS) of the observed nonGaussian data. Cumulants of vector processes are defined using a Kronecker product formulation, and consistency of their sample estimators is addressed. Identifiability results in connection with the HOS-based parameter estimation of causal and noncausal multivariate ARMA processes are established. Estimates of the parameters of causal ARMA models are obtained as the solution to a set of linear equations, whereas those of noncausal ARMA models are obtained as the solution to a cumulant matching algorithm. Conventional approaches based on second-order statistics can identify a multichannel system only to within post multiplication by a unimodular matrix. HOS-based methods yield solutions that are unique to within post-multiplication by an (extended) permutation matrix; additionally, the multiminimum phase assumption can be relaxed, and the observations may be contaminated with colored Gaussian noise. Frequency-domain methods for nonparametric system identification are discussed briefly. Simulations results validating the multichannel parameter estimation algorithms are provided