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Local Likelihood for non-parametric ARCH(1) models

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  • Francesco Audrino

Abstract

We propose a non-parametric local likelihood estimator for the log-transformed autoregressive conditional heteroscedastic (ARCH) (1) model. Our non-parametric estimator is constructed within the likelihood framework for non-Gaussian observations: it is different from standard kernel regression smoothing, where the innovations are assumed to be normally distributed. We derive consistency and asymptotic normality for our estimators and show, by a simulation experiment and some real-data examples, that the local likelihood estimator has better predictive potential than classical local regression. A possible extension of the estimation procedure to more general multiplicative ARCH(p) models with p > 1 predictor variables is also described. Copyright 2005 Blackwell Publishing Ltd.

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Bibliographic Info

Article provided by Wiley Blackwell in its journal Journal of Time Series Analysis.

Volume (Year): 26 (2005)
Issue (Month): 2 (03)
Pages: 251-278

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Handle: RePEc:bla:jtsera:v:26:y:2005:i:2:p:251-278

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Web page: http://www.blackwellpublishing.com/journal.asp?ref=0143-9782

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Cited by:
  1. Francesco Audrino & Peter Bühlmann, 2009. "Splines for financial volatility," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(3), pages 655-670.

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