Dovonon, Prosper and Renault, Eric (2011): Testing for Common GARCH Factors.

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Abstract
This paper proposes a test for common GARCH factors in asset returns. Following Engle and Kozicki (1993), the common GARCH factors property is expressed in terms of testable overidentifying moment restrictions. However, as we show, these moment conditions have a degenerate Jacobian matrix at the true parameter value and therefore the standard asymptotic results of Hansen (1982) do not apply. We show in this context that the Hansen's (1982) Jtest statistic is asymptotically distributed as the minimum of the limit of a certain empirical process with a markedly nonstandard distribution. If two assets are considered, this asymptotic distribution is a halfhalf mixture of chisquares with H1 and H degrees of freedom, where H is the number of moment conditions, as opposed to a chisquare with H1 degree of freedom. With more than two assets, this distribution lies between the chisquare with Hp and the chisquare with H degrees of freedom (p, the number of parameters) and both bounds are conditionally sharp. These results show that ignoring the lack of first order identification of the moment condition model leads to oversized tests with possibly increasing overrejection rate with the number of assets. A Monte Carlo study illustrates these findings.
Item Type:  MPRA Paper 

Original Title:  Testing for Common GARCH Factors 
Language:  English 
Keywords:  GARCH factors, Nonstandard asymptotics, GMM, GMM overidenti fication test, identifi cation, first order identification 
Subjects:  C  Mathematical and Quantitative Methods > C0  General > C01  Econometrics 
Item ID:  40224 
Depositing User:  Prosper Dovonon 
Date Deposited:  23. Jul 2012 14:16 
Last Modified:  16. Feb 2013 00:40 
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URI:  http://mpra.ub.unimuenchen.de/id/eprint/40224 