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TAIL INDEX OF AN AR(1) MODEL WITH ARCH(1) ERRORS

Published online by Cambridge University Press:  21 February 2013

Ngai Hang Chan,
Deyuan Li,
Liang Peng and
Rongmao Zhang
Ngai Hang Chan
Affiliation:
Chinese University of Hong Kong
Deyuan Li
Affiliation:
Fudan University
Liang Peng
Affiliation:
Georgia Institute of Technology
Rongmao Zhang*
Affiliation:
Zhejiang University
*
*Address correspondence to Rongmao Zhang, Department of Mathematics, Zhejiang University, Hangzhou, 310027, China; e-mail: rmzhang@zju.edu.cn.
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Abstract

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Relevant sample quantities such as the sample autocorrelation function and extremes contain useful information about autoregressive time series with heteroskedastic errors. As these quantities usually depend on the tail index of the underlying heteroskedastic time series, estimating the tail index becomes an important task. Since the tail index of such a model is determined by a moment equation, one can estimate the underlying tail index by solving the sample moment equation with the unknown parameters being replaced by their quasi-maximum likelihood estimates. To construct a confidence interval for the tail index, one needs to estimate the complicated asymptotic variance of the tail index estimator, however. In this paper the asymptotic normality of the tail index estimator is first derived, and a profile empirical likelihood method to construct a confidence interval for the tail index is then proposed. A simulation study shows that the proposed empirical likelihood method works better than the bootstrap method in terms of coverage accuracy, especially when the process is nearly nonstationary.

Information

Type
ARTICLES
Information
Econometric Theory , Volume 29 , Issue 5 , October 2013, pp. 920 - 940
Copyright
Copyright © Cambridge University Press 2013 

Footnotes

We would like to thank the co-editor and two anonymous referees for their careful readings and helpful suggestions. Research was supported in part by grants from HKSAR-RGC-GRF: 400306, 400408, and 400410; HKSAR-RGC-CRF: CityU8/CRF/09; NSA: H98230-10-1-0170; NSF: DMS-1005336; NSFC: 11171074 and 10801118; and the Ph.D. Programs Foundation of the Ministry of Education of China (200803351094).

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