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

Peter M. Robinson·Paolo Zaffaroni
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Abstract

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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Peter M. Robinson, Paolo Zaffaroni. 2006-07-31. Pseudo-maximum likelihood estimation of ARCH$(\infty)$ models. https://doi.org/10.1214/009053606000000245

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