Model diagnostics and validation for linear model fitting using higher-order statistics

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 some simple frequency-domain tests that are applicable to both third-order and fourth-order statistics-based model fitting unlike existing tests. A computer simulation example is presented to illustrate the proposed tests.