On asymptotic theory for ARCH(∞) models

ARCH(∞) models nest a wide range of ARCH and GARCH models in- cluding models with long memory in volatility. Existing work assumes the existence of second moments. However, the FIGARCH model, 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 pa- per 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