Testing for Common Conditionally Heteroskedastic Factors
提出一种检验资产收益中共同条件异方差特征的方法，发现标准检验统计量渐近分布非标准，蒙特卡洛模拟显示忽略此问题会导致过度拒绝。
This paper proposes a test for common conditionally heteroskedastic (CH) features in asset returns. Following Engle and Kozicki (1993), the common CH features property \nis expressed in terms of testable overidentifying moment restrictions. However, as we show, these moment conditions have a degenerate Jacobian matrix at the true parameter \nvalue 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 \ndistributed 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 \nfifty–fifty mixture of χ2 H−1 and χ2 H, whereH is the number of moment conditions, as opposed to a χ2 \nH−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 \nfirst-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.