A consistent cumulant-based NCARMA estimator

The problem of estimating the order and parameters of a noncausal autoregressive moving average (NCARMA) model excited by an unobservable independent and identically distributed process is addressed. The observed output may be corrupted by additive colored Gaussian noise. A fourth-order cumulant based parameter estimator is proposed, and the consistency of the estimator is established. The proposed algorithm leads readily to an order determination algorithm as well. The algorithms can be extended to higher-orders, but not to third-order cumulants. Once the AR parameters have been estimated, the AR-compensated residual time-series may be estimated