An efficient, multi stage, linear identification method for ARMA processes

A new method for estimating the parameters of an ARMA system is considered. The method involves three linear least squares estimations: in the first an autoregressive model is fitted to the output sequence, yielding an estimate of the "white noise" input sequence; in the second an ARMA model is fitted to the output and estimated input sequences (Durbin\´s estimator); in the third an ARMA model is fitted to filtered versions of the output and estimated input sequences, the filter being obtained from Durbin\´s estimator. The consistency of the resultant estimator is established and some comments on its efficiency are made.