Peter M Robinson and Paolo Zaffaroni

Published October 2005

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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(8) processes are established. We require the ARCH weights to decay at least hyperbolically, with a faster rate needed for the central limit theorem than for the law of large numbers. Various rates are illustrated in examples of particular parameteriza- tions in which our conditions are shown to be satisfied.