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Local Likelihood for non‐parametric ARCH(1) models
Author(s) -
Audrino Francesco
Publication year - 2005
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.2005.00400.x
Subject(s) - mathematics , heteroscedasticity , estimator , kernel smoother , statistics , nonparametric regression , autoregressive model , arch , asymptotic distribution , econometrics , kernel method , computer science , artificial intelligence , civil engineering , radial basis function kernel , support vector machine , engineering
. 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.