CONSISTENT ORDER SELECTION FOR NONCAUSAL AUTOREGRESSIVE MODELS VIA HIGHER-ORDER STATISTICS

The problem of determining the order of a noncausal autoregressive (AR) model given the noisy observations of the system output is considered. The system is driven by an i.i.d. (independent and identically distributed) non-Gaussian sequence that is not observed. The measurement noise is additive, i.i.d., and possibly non-Gaussian. We propose a new method for order selection and prove its strong consistency. Unlike a previously proposed method, the new method does not require testing of 2p candidate models where p is the number of system poles. Some recently developed fundamental results concerning the recovery of the poles of a causal system from the third-order statistics of the system output play a crucial role in this paper. The proposed method is illustrated by a numerical example. © 1990.