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Recently, a model identification system ( MIS ) has been studied for ARMA parameter estimation. Since in MIS an estimator with a high-order ARMA parameter and a model reduction algorithm are used, the tracking ability of the spectral estimation is good. However in real speech analysis, estimation errors are caused by the use of a low-pass filter for A/D conversion. In order to compensate for such errors we propose a weighted MIS ( WMIS ) which includes a compensation for the characteristics of the low-pass filter. The WMIS estimates the input of the reference model and time-varying ARMA parameters, and achieves the property of rapid convergence by using a high-order model. Furthermore the algorithm for minimum realization is shown as a model reduction algorithm. The proposed algorithms are applied to synthetic speech and real speech, and it is shown that the estimated spectra sufficiently represent the variation of formants without jitters in the high-frequency part.