A multistep iterative and fast recursive algorithm, for autoregressive moving average, (ARMA) spectral estimation is presented. The AR parameters of an ARMA process are estimated using the extended instrumental variable (EIV) method. The optimal choice of instruments, prefilter, and weighting matrix is investigated. A bootstrapping procedure that has computational convenience is proposed for the algorithm. The statistical analysis and experiments show that the optimal IV estimate is unbiased, consistent, efficient, asymptotically normal, and equivalent to the maximum-likelihood (ML) estimate and the prediction error (PE) estimate; and the proposed algorithm has the advantages of sharper resolution, less frequency bias, and better efficiency of convergence.
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