Cumulant-based order determination of non-Gaussian ARMA models

The objective is the order determination of non-Gaussian and nonminimum phase autoregressive moving average (ARMA) models, using higher-order cumulant statistics. The two methods developed assume knowledge of upper bounds on the ARMA orders. The first method performs a linear dependence search among the columns of a higher-order statistics matrix by means of the Gram-Schmidt orthogonalization procedure. In the second method, the order of the AR part is found as the rank of the matrix formed by the higher-order statistics sequence. For numerically robust rank determination the singular value decomposition approach is adopted. The argument principle and samples of the polyspectral phase are used to obtain the relative degree of the ARMA model, from which the order of the MA part can be determined. Statistical analysis is included for determining the correct MA order with high probability, when estimates of third-order cumulants are only available. Simulations are used to verify the performance of the methods and compare autocorrelation with cumulant-based order determination approaches