Strong consistency and asymptotic normality of the Gaussian pseudo maximum likelihood estimate of the parameters in a wide class of ARCH(oo) processes are established. The conditions are shown to hold in case of expo nential 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(1) models / Zaffaroni, Paolo; PETER M., Robinson. - In: ANNALS OF STATISTICS. - ISSN 0090-5364. - 34:(2006), pp. 1049-1074. [10.1214/009053606000000245]
Pseudo-maximum likelihood estimation of ARCH(1) models
ZAFFARONI, Paolo;
2006
Abstract
Strong consistency and asymptotic normality of the Gaussian pseudo maximum likelihood estimate of the parameters in a wide class of ARCH(oo) processes are established. The conditions are shown to hold in case of expo nential 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.File allegati a questo prodotto
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