A comparison of numerator estimators for ARMA spectra

This correspondence investigates the problems of estimating the numerator spectrum corresponding to an ARMA time series model once the denominator spectrum (i.e., the AR coefficients) has been estimated. A general form for an estimator of the numerator spectral (NS) coefficients is developed first. Six NS estimators from the recent literature are then compared by fitting them into this general framework and extracting their particular characteristics. It is shown that some methods are special cases of other methods, and that several of these methods are asymptotically equivalent.