Testing for Common Conditionally Heteroskedastic Factors

Prosper Dovonon, Eric Renault

Research output: Contribution to journalArticleResearchpeer-review

19 Citations (Scopus)


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 χ2H-1 and χ2H, where H is the number of moment conditions, as opposed to a χ2H-1. With more than two assets, this distribution lies between the χ2H-p and χ2H (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.

Original languageEnglish
Pages (from-to)2561-2586
Number of pages26
Issue number6
Publication statusPublished - Nov 2013
Externally publishedYes


  • Common features
  • First-order identification
  • GARCH factors
  • GMM
  • GMM overidentification test
  • Identification
  • Nonstandard asymptotics

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