## The Annals of Statistics

### Pseudo-maximum likelihood estimation of ARCH(∞) models

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 10 July 2006

https://projecteuclid.org/euclid.aos/1152540742

Digital Object Identifier
doi:10.1214/009053606000000245

Mathematical Reviews number (MathSciNet)
MR2278351

Zentralblatt MATH identifier
1113.62107

#### Citation

Robinson, Peter M.; Zaffaroni, Paolo. Pseudo-maximum likelihood estimation of ARCH(∞) models. Ann. Statist. 34 (2006), no. 3, 1049--1074. doi:10.1214/009053606000000245. https://projecteuclid.org/euclid.aos/1152540742

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