Weighted Least Squares Estimators on the Frequency Domain for the Parameters of a Time Series
RICE UNIV HOUSTON TX DEPT OF MATHEMATICAL SCIENCES
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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 periodograms and the spectrum of the series. Under mild conditions, the estimate is shown to be strongly consistent. The asymptotic distribution of the estimate is also obtained. With a proper choice of weighting function, the estimate has the same asymptotic distribution as the one for the maximum likelihood estimate. Simulations were carried out to evaluate the performance of the estimate.
- Statistics and Probability