The Annals of Statistics

Asymptotic Properties of the LSE in a Regression Model with Long-Memory Stationary Errors

Yoshihiro Yajima

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Abstract

We consider asymptotic properties of the least squares estimator (LSE) in a regression model with long-memory stationary errors. First we derive a necessary and sufficient condition that the LSE be asymptotically efficient relative to the best linear unbiased estimator (BLUE). Then we derive the asymptotic distribution of the LSE under a condition on the higher-order cumulants of the white-noise process of the errors.

Article information

Source
Ann. Statist., Volume 19, Number 1 (1991), 158-177.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176347975

Digital Object Identifier
doi:10.1214/aos/1176347975

Mathematical Reviews number (MathSciNet)
MR1091844

Zentralblatt MATH identifier
0728.62085

JSTOR
links.jstor.org

Subjects
Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 62J05: Linear regression

Keywords
Long-memory models regression least squares estimators

Citation

Yajima, Yoshihiro. Asymptotic Properties of the LSE in a Regression Model with Long-Memory Stationary Errors. Ann. Statist. 19 (1991), no. 1, 158--177. doi:10.1214/aos/1176347975. https://projecteuclid.org/euclid.aos/1176347975


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