Strong consistency and asymptotic normality of the Gaussian pseudo-maximum likelihood estimate of the parameters in a wide class of ARCH(∞) processes are established. The conditions are shown to hold in case of exponential 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.
"Pseudo-maximum likelihood estimation of ARCH(∞) models." Ann. Statist. 34 (3) 1049 - 1074, June 2006. https://doi.org/10.1214/009053606000000245