Pseudo-maximum likelihood estimation of ARCH(infinity) models

Abstract

Strong consistency and asymptotic normality of the Gaussian pseudo maximum likelihood estimate of the parameters in a wide class of ARCH(oo) processes are established. The conditions are shown to hold in case of expo nential and hyperbolic decay in the ARCH weights, though in the latter case a faster decay rate is required for the central limit theorem than for the law of large numbers. Particular parameterizations are discussed.