CONSISTENT PARAMETER-ESTIMATION FOR NONCAUSAL AUTOREGRESSIVE MODELS VIA HIGHER-ORDER STATISTICS

The problem of estimating the parameters of a non-causal 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. A parameter estimator that involves simultaneous matching of data autocorrelations and third-order auto-cumulants was recently proposed for the estimation of the parameters of non-causal AR models. In the proposed method the maximum cumulant lag used in cumulant matching was specified as "large" but finite. In this paper we give a specific lower bound to the maximum cumulant lag, and we prove the strong consistency of the parameter estimator under the specified choice of lags. 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. © 1990.