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TOWARD A UNIFIED INTERVAL ESTIMATION OF AUTOREGRESSIONS

Published online by Cambridge University Press:  25 November 2011

Ngai Hang Chan ,
Deyuan Li  and
Liang Peng
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Abstract

An empirical likelihood–based confidence interval is proposed for interval estimations of the autoregressive coefficient of a first-order autoregressive model via weighted score equations. Although the proposed weighted estimate is less efficient than the usual least squares estimate, its asymptotic limit is always normal without assuming stationarity of the process. Unlike the bootstrap method or the least squares procedure, the proposed empirical likelihood–based confidence interval is applicable regardless of whether the underlying autoregressive process is stationary, unit root, near-integrated, or even explosive, thereby providing a unified approach for interval estimation of an AR(1) model to encompass all situations. Finite-sample simulation studies confirm the effectiveness of the proposed method.

Type
Brief Report
Information
Econometric Theory , Volume 28 , Issue 3 , June 2012 , pp. 705 - 717
Copyright
Copyright © Cambridge University Press 2011

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Footnotes

We thank three anonymous referees, the editor, and the co-editor Giuseppe Cavaliere for helpful references and constructive suggestions, which led to an improved version of this note. This research was supported in part by grants from HKSAR-RGC-GRF nos. 400306, 400308, and 400410, NSA grant no. H98230-10-1-0170, NSF grant no. DMS1005336, and NNSFC grant no. 10801038.

References

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