Annals of Statistics

An Optimality Property of the Least-Squares Estimate of the Parameter of the Spectrum of a Purely Nondeterministic Time Series

Paul V. Kabaila

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Abstract

Whittle has proved that the least-squares estimator of a scalar parameter of the spectrum of a purely nondeterministic time series possesses a certain optimality property independently of the distribution of the residuals. In this paper we furnish a proof in full detail of the corresponding result for a vector parameter and also provide some examples which illustrate the application of the result.

Article information

Source
Ann. Statist., Volume 8, Number 5 (1980), 1082-1092.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176345145

Digital Object Identifier
doi:10.1214/aos/1176345145

Mathematical Reviews number (MathSciNet)
MR585706

Zentralblatt MATH identifier
0447.62097

JSTOR
links.jstor.org

Subjects
Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]

Keywords
Time-series least-squares estimation efficiency

Citation

Kabaila, Paul V. An Optimality Property of the Least-Squares Estimate of the Parameter of the Spectrum of a Purely Nondeterministic Time Series. Ann. Statist. 8 (1980), no. 5, 1082--1092. doi:10.1214/aos/1176345145. https://projecteuclid.org/euclid.aos/1176345145


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