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GENERALIZED AUTOREGRESSIVE CONDITIONAL CORRELATION

Published online by Cambridge University Press:  09 July 2008

Michael McAleer ,
Felix Chan ,
Suhejla Hoti  and
Offer Lieberman
Michael McAleer
Affiliation:
University of Western Australia and Yokohama National University
Felix Chan
Affiliation:
Curtin University of Technology
Suhejla Hoti
Affiliation:
University of Western Australia
Offer Lieberman*
Affiliation:
University of Haifa
*
Address correspondence to Offer Lieberman, Department of Economics, University of Haifa, Haifa 31905, Israel; e-mail: [email protected]
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Abstract

This paper develops a generalized autoregressive conditional correlation (GARCC) model when the standardized residuals follow a random coefficient vector autoregressive process. As a multivariate generalization of the Tsay (1987, Journal of the American Statistical Association 82, 590–604) random coefficient autoregressive (RCA) model, the GARCC model provides a motivation for the conditional correlations to be time varying. GARCC is also more general than the Engle (2002, Journal of Business & Economic Statistics 20, 339–350) dynamic conditional correlation (DCC) and the Tse and Tsui (2002, Journal of Business & Economic Statistics 20, 351–362) varying conditional correlation (VCC) models and does not impose unduly restrictive conditions on the parameters of the DCC model. The structural properties of the GARCC model, specifically, the analytical forms of the regularity conditions, are derived, and the asymptotic theory is established. The Baba, Engle, Kraft, and Kroner (BEKK) model of Engle and Kroner (1995, Econometric Theory 11, 122–150) is demonstrated to be a special case of a multivariate RCA process. A likelihood ratio test is proposed for several special cases of GARCC. The empirical usefulness of GARCC and the practicality of the likelihood ratio test are demonstrated for the daily returns of the Standard and Poor's 500, Nikkei, and Hang Seng indexes.

Type
Research Article
Information
Econometric Theory , Volume 24 , Issue 6 , December 2008 , pp. 1554 - 1583
Copyright
Copyright © Cambridge University Press 2008

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