The Annals of Statistics

Pseudo-maximum likelihood estimation of ARCH(∞) models

Peter M. Robinson and Paolo Zaffaroni

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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.

Article information

Ann. Statist., Volume 34, Number 3 (2006), 1049-1074.

First available in Project Euclid: 10 July 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 62F12: Asymptotic properties of estimators

ARCH(∞) models pseudo-maximum likelihood estimation asymptotic inference


Robinson, Peter M.; Zaffaroni, Paolo. Pseudo-maximum likelihood estimation of ARCH(∞) models. Ann. Statist. 34 (2006), no. 3, 1049--1074. doi:10.1214/009053606000000245.

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