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Journal of Financial Econometrics Advance Access published online on August 18, 2009
Journal of Financial Econometrics, doi:10.1093/jjfinec/nbp007
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© The Author 2009. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oupjournals.org

Shifts in Individual Parameters of a GARCH Model

Pedro Galeano
     Universidad Carlos III de Madrid

Ruey S. Tsay
     University of Chicago

Address correspondence to Pedro Galeano, Departamento de Estadística, Universidad Carlos III de Madrid, 28903 Getafe, Madrid, Spain, or e-mail: pedro.galeano{at}uc3m.es

JEL Classification: C5, G1


  Abstract

Most asset return series, especially those in high frequency, show high excess kurtosis and persistence in volatility that cannot be adequately described by the generalized conditional heteroscedastic (GARCH) model, even with heavy-tailed innovations. Many researchers have argued that these characteristics are due to shifts in volatility that may be associated with significant economic events such as financial crises. Indeed, several authors have investigated the case of pure structural changes, in which all of the parameters in the GARCH model are assumed to change simultaneously. In this paper, we take an alternative approach by studying the case in which changes occur in individual parameters of a GARCH model. We investigate the impacts of such changes on the underlying return series and its volatility, and propose an iterative procedure to detect them. In all cases, the changes affect permanently the level of the volatility, but in some cases, the changes also alter the dynamic structure of the volatility series. Monte Carlo experiments are used to investigate the performance of the proposed procedure in finite samples, and real examples are used to demonstrate the impacts of detected volatility changes and the efficacy of the proposed procedure. Practical implications of the parameter changes in financial applications are also discussed.

KEYWORDS: change point detection, excess Kurtosis, GARCH model, high persistence, parameter change

The first author acknowledges financial support by MEC project MTM2008-03010 and the Xunta de Galicia project PGIDIT06PXIB207009PR. The second author thanks the financial support by the National Science Foundation and the Booth School of Business, University of Chicago.

Received September 4, 2007; revised March 27, 2008; accepted May 21, 2009


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