Pseudo-maximum likelihood estimation of ARCH$(\infty)$ models

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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$(\infty)$ 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.
Published at http://dx.doi.org/10.1214/009053606000000245 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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Statistics Theory, 62M10 (Primary) 62F12 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/131130

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0607798
 http://arxiv.org/abs/math/0607798
 Annals of Statistics 2006, Vol. 34, No. 3, 1049-1074
 doi:10.1214/009053606000000245

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