Testing That Some GARCH Coefficients are Equal to Zero

Abstract

The asymptotic distribution of the quasi-maximum likelihood (QML) estimator for generalized autoregressive conditional heteroskedastic (GARCH) processes is not standard when the true parameter have zero coefficients. This asymptotic distribution is the projection of a normal vector distribution onto a convex cone. We show that the QML estimator does not converge to its asymptotic distribution locally uniformly. Using these results, we consider the problem of testing that one or several GARCH coefficients are equal to zero. The null distribution and the local asymptotic powers of the Wald, score and quasi-likelihood ratio tests are derived. The one-sided nature of the problem is exploited and asymptotic optimality issues are addressed.