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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.

Suggested Citation

  • Francesco Audrino, 2005. "Local Likelihood for non‐parametric ARCH(1) models," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(2), pages 251-278, March.
    • Handle: RePEc:bla:jtsera:v:26:y:2005:i:2:p:251-278
    DOI: 10.1111/j.1467-9892.2005.00400.x
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    References listed on IDEAS

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    1. HÄRDLE, Wolfgang & VIEU, Philippe, 1992. "Kernel regression smoothing of time series," LIDAM Reprints CORE 981, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    5. Franke, Jürgen & Holzberger, Harriet & Müller, Marlene, 2002. "Nonparametric estimators of GARCH processes," SFB 373 Discussion Papers 2002,43, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    6. Carroll, Raymond J. & Härdle, Wolfgang & Mammen, Enno, 2002. "Estimation In An Additive Model When The Components Are Linked Parametrically," Econometric Theory, Cambridge University Press, vol. 18(4), pages 886-912, August.
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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, June.
    2. Arash Nademi & Rahman Farnoosh, 2014. "Mixtures of autoregressive-autoregressive conditionally heteroscedastic models: semi-parametric approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(2), pages 275-293, February.

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