Large deviations for the Yule–Walker estimator of near critical autoregressive processes

The large deviation principle is established for the Yule–Walker estimator of the near critical order one autoregressive process. The rate function is identified explicitly. Our result shows that, at the exponential scale, one cannot distinguish between near critical and the critical Yule–Walker est...

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Bibliographic Details
Published inStatistics & probability letters Vol. 214; p. 110196
Main Authors Wang, Xiaochang, Feng, Shui, Guo, Yiping, Rémillard, Bruno N.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.11.2024
Subjects
Large deviation
Near critical autoregressive process
Unit root tests
Yule–Walker and OLS estimators
62M10
Yule–Walker and OLS estimators
Near critical autoregressive process
Unit root tests
60F10
Large deviation
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Summary:The large deviation principle is established for the Yule–Walker estimator of the near critical order one autoregressive process. The rate function is identified explicitly. Our result shows that, at the exponential scale, one cannot distinguish between near critical and the critical Yule–Walker estimators.
ISSN:0167-7152
1879-2103
DOI:10.1016/j.spl.2024.110196