On asymptotic theory for ARCH(∞) models

ARCH(∞) models nest a wide range of ARCH and GARCH models including models with long memory in volatility. The existing literature on such models is quite restrictive in terms of existence of moments. However, the popular FIGARCH, one version of a long memory in volatility model, does not have finite second moments and rarely satisfies the moment conditions of the existing literature. This paper considerably weakens the moment assumptions of a general ARCH(∞) class of models, and develops the theory for consistency and asymptotic normality of the quasi maximum likelihood estimator.