Weighted Least Squares Estimators on the Frequency Domain for the Parameters of a Time Series

Abstract

A procedure for estimating the parameters of a time series is proposed. The estimate minimizes a criterion function which is the weighted sum of squares of the distances between the periodogram and the spectrum of the series. Under regularity conditions, the estimate is shown to be strongly consistent. The asymptotic distribution of the estimate is also obtained. It is shown that, for a Gaussian process, an asymptotically efficient estimate can be obtained by using an iteratively reweighted procedure.