Cumulant Based Parameter Estimation Of Linear Systems Of Nonminimum Phase

One of the basic problems in multivariate time series model fitting, is that of estimating ARMA models from the outputs using their statistics. Nonminimum phase ARMA models are not identifiable by using multichannel parameter estimation approaches based on second-order statistics, because these are limited to Gaussian processes. It is widely known that, if time series are non-Gaussian, then nonminimum phase parametric models are identifiable from the time series using their higher-order cumulants. This paper propose a procedure for estimating the coefficient matrices of multichannel nonminimum phase ARMA models, and give a recursive algorithm for calculating the AR coefficient matrices. A simulation example is given to illustrate the results of the proposed procedure.