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EMPIRICAL LIKELIHOOD FOR GARCH MODELS

Published online by Cambridge University Press:  15 March 2006

Ngai Hang Chan  and
Shiqing Ling
Ngai Hang Chan
Affiliation:
Chinese University of Hong Kong
Shiqing Ling
Affiliation:
Hong Kong University of Science and Technology
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Abstract

This paper develops an empirical likelihood approach for regular generalized autoregressive conditional heteroskedasticity (GARCH) models and GARCH models with unit roots. For regular GARCH models, it is shown that the log empirical likelihood ratio statistic asymptotically follows a χ2 distribution. For GARCH models with unit roots, two versions of the empirical likelihood methods, the least squares score and the maximum likelihood score functions, are considered. For both cases, the limiting distributions of the log empirical likelihood ratio statistics are established. These two statistics can be used to test for unit roots under the GARCH framework. Finite-sample performances are assessed through simulations for GARCH models with unit roots.This research was supported in part by Hong Kong Research grants Council Grants CUHK4043/02P and HKUST6273/03H. The authors thank two referees and the Co-Editor, Bruce Hansen, for insightful and helpful comments about the relationship between QMLE and MELE, which led to substantial improvement of the presentation. Computational assistance from Jerry Wong and Chun-Yip Yau is also gratefully acknowledged.

Type
Research Article
Information
Econometric Theory , Volume 22 , Issue 3 , June 2006 , pp. 403 - 428
Copyright
© 2006 Cambridge University Press

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