Nonlinear H-ARMA models

We present some aspects of non-Gaussian H-ARMA models. After recalling that an H-ARMA process is obtained by passing an ARMA process through a Hermite polynomial nonlinearity, we describe the theoretical analysis of their cumulants and cumulant spectra. The main advantage of this kind of model is that the cumulant structure of the output can be deduced directly from the input covariance sequence. We give the analytic forms of these cumulants, together with some comments on their estimation. Then, we present the problems we are facing concerning the identification of the model´s parameters, and give a first (and naive) method for their estimation. We give some results obtained on synthetic data and finally conclude with some remarks on this class of processes