The Annals of Statistics

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

Shean-Tsong Chiu

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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.

Article information

Source
Ann. Statist., Volume 16, Number 3 (1988), 1315-1326.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176350963

Digital Object Identifier
doi:10.1214/aos/1176350963

Mathematical Reviews number (MathSciNet)
MR959204

Zentralblatt MATH identifier
0649.62091

JSTOR
links.jstor.org

Subjects
Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 62M15: Spectral analysis 62F10: Point estimation

Keywords
Time series weighted least squares estimation periodogram spectrum cumulants

Citation

Chiu, Shean-Tsong. Weighted Least Squares Estimators on the Frequency Domain for the Parameters of a Time Series. Ann. Statist. 16 (1988), no. 3, 1315--1326. doi:10.1214/aos/1176350963. https://projecteuclid.org/euclid.aos/1176350963


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