Higher-order asymptotic properties of QML in β-ARCH and μ-ARCH models

In this paper we provide O(T− 1) bias and asymptotic variance expressions for the quasi-maximum likelihood (QML) estimators of the parameters of β-ARCH and μ-ARCH models. We show that for some combinations of parameters, large biases and large variances occur. These types of results do not appear in regular ARCH models. We also point out some nondifferentiability and identification issues.