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June 2006 Pseudo-maximum likelihood estimation of ARCH(∞) models
Peter M. Robinson, Paolo Zaffaroni
Ann. Statist. 34(3): 1049-1074 (June 2006). 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.

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Peter M. Robinson. Paolo Zaffaroni. "Pseudo-maximum likelihood estimation of ARCH(∞) models." Ann. Statist. 34 (3) 1049 - 1074, June 2006. https://doi.org/10.1214/009053606000000245

Information

Published: June 2006
First available in Project Euclid: 10 July 2006

zbMATH: 1113.62107
MathSciNet: MR2278351
Digital Object Identifier: 10.1214/009053606000000245

Subjects:
Primary: 62M10
Secondary: 62F12

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

Rights: Copyright © 2006 Institute of Mathematical Statistics

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Vol.34 • No. 3 • June 2006
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