Abstract

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 χ2 H−1 and χ2 H, whereH is the number of moment conditions, as opposed to a χ2
H−1.With more than two assets, this distribution lies between the χ2 H−p and χ2 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.