Maximum likelihood estimation of the parameters of nonminimum phase and noncausal ARMA models

The well-known prediction-error-based maximum likelihood (PEML) method can only handle minimum phase ARMA models. This likelihood (BFML) method, which can handle nonminimum phase and noncausal ARMA models. The BFML method is identical to the PEML method in the case of a minimum phase ARMA model, and it turns out that the BFML method incorporates a noncausal ARMA filter with poles outside the unit circle for estimation of the parameters of a causal, nonminimum phase ARMA model. paper presents a new method known as the back-filtering-based maximum € ( e ) = F t ( O ) ' y . (4) Note that the back-filtered sequence depends on 8; see Fig. 1. The BFML estimate OBF*\ILF of the true parameter vector & R L F is ( 5 ) n;=, f e ( , t ) ( d T 1 : @ ) : O ) ldet(RFI)l . H B E L I L E = aignidx