On Asymptotic Theory for ARCH (∞) Models
本文放宽了ARCH(∞)类模型的矩条件假设，证明了拟极大似然估计量的一致性和渐近正态性，适用于长记忆波动率模型等二阶矩不存在的情形。
Autoregressive conditional heteroskedasticity (ARCH)( ) models nest a wide range of ARCH and generalized ARCH models including models with long memory in volatility. Existing work assumes the existence of second moments. However, the fractionally integrated generalized ARCH 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 article 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.