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

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

2006-07-31

arxiv.org/abs/math/0607798v1

Annals of Statistics 2006, Vol. 34, No. 3, 1049-1074

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053606000000245 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053606000000245

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.

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