Linear model validation and order selection using higher order statistics

There exists several methods for fitting linear models to linear stationary nonGaussian signals using higher order statistics. The models are fitted under certain assumptions on the data and the underlying (true) model. This paper is devoted to the problem of model validation, i.e., to checking if the fitted linear model is consistent with the underlying basic assumptions. Model order selection is a by-product of the solution. We provide a fairly easy-to-apply statistical test based on the asymptotic properties of the bispectrum of the inverse filtered data. Computer simulation results are presented for both linear model validation and model order selection. The proposed model order selection approach is compared with an existing order selection method based upon rank testing via singular value decomposition