Model validation and order selection for linear model fitting using third- and fourth-order cumulants

Given a linear stationary non-Gaussian signal, suppose that we fit a linear model using higher order statistics and one of several existing methods. The model is fitted under certain assumptions on the data and the underlying (true) model. Having obtained a model, how do we know if the fitted model is "good?" This paper is devoted to the problem of model diagnostics and validation. We propose frequency-domain tests that are applicable to both third- and fourth-order statistics-based model fitting unlike existing tests. Model order selection is a byproduct of the model validation approach. Two computer simulation examples are presented to illustrate the proposed tests.