Information theoretic criteria for non-Gaussian ARMA order determination and parameter estimation

The problem of determining the orders and parameters of autoregressive moving average (ARMA) processes with an unknown but non-Gaussian probability density function is addressed. Asymptotically optimal, information theoretic criteria are developed based on higher-order statistics of the observed processes. The proposed algorithms rely upon sample cumulants, or polyspectra, and allow non-minimum phase and non-causal models unlike the conventional second-order correlation based methods. Unlike the linear rank-based cumulant methods, the nonlinear information theoretic type methods do not require subjective thresholding and yield strongly consistent estimators for the ARMA orders as well as the parameters. Simulation examples illustrate the feasibility of the theory.<>