Pseudo-maximum likelihood estimation of ARCH(∞) models
Peter M. Robinson, Paolo Zaffaroni
The Annals of Statistics · 2006 · Volume 34 · Issue 3
DOI: 10.1214/009053606000000245
Abstract
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.
Keywords
62F12, 62M10, ARCH(∞) models, asymptotic inference, pseudo-maximum likelihood estimation
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