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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.