Local Likelihood for non‐parametric ARCH(1) models

Francesco Audrino

Journal of Time Series Analysis, 2005, vol. 26, issue 2, 251-278

Abstract: 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.

Date: 2005
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https://doi.org/10.1111/j.1467-9892.2005.00400.x

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Persistent link: https://EconPapers.repec.org/RePEc:bla:jtsera:v:26:y:2005:i:2:p:251-278

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