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Testing for Common Conditionally Heteroskedastic Factors
Author(s) -
Dovo Prosper,
Renault Eric
Publication year - 2013
Publication title -
econometrica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 16.7
H-Index - 199
eISSN - 1468-0262
pISSN - 0012-9682
DOI - 10.3982/ecta10082
Subject(s) - heteroscedasticity , mathematics , moment (physics) , context (archaeology) , asymptotic distribution , test statistic , econometrics , statistics , statistical hypothesis testing , estimator , paleontology , physics , classical mechanics , biology
This paper proposes a test for common conditionally heteroskedastic (CH) features in asset returns. Following Engle and Kozicki (1993), the common CH features 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 Hansen's (1982) J ‐test statistic is asymptotically distributed as the minimum of the limit of a certain random process with a markedly nonstandard distribution. If two assets are considered, this asymptotic distribution is a fifty–fifty mixture of χ 2 H −1 and χ 2 H , where H is the number of moment conditions, as opposed to a χ 2 H −1 . With more than two assets, this distribution lies between the χ 2 H − p and χ 2 H ( p denotes the number of parameters). These results show that ignoring the lack of first‐order identification of the moment condition model leads to oversized tests with a possibly increasing overrejection rate with the number of assets. A Monte Carlo study illustrates these findings.