# Adaptive density estimation for general ARCH models

Abstract : We consider a model $Y_t=\sigma_t\eta_t$ in which $(\sigma_t)$ is not independent of the noise process $(\eta_t)$, but $\sigma_t$ is independent of $\eta_t$ for each $t$. We assume that $(\sigma_t)$ is stationary and we propose an adaptive estimator of the density of $\ln(\sigma^2_t)$ based on the observations $Y_t$. Under various dependence structures, the rates of this nonparametric estimator coincide with the minimax rates obtained in the i.i.d. case when $(\sigma_t)$ and $(\eta_t)$ are independent, in all cases where these minimax rates are known. The results apply to various linear and non linear ARCH processes.
Keywords :
Type de document :
Pré-publication, Document de travail
2006
Domaine :

Littérature citée [31 références]

https://hal.archives-ouvertes.fr/hal-00101417
Contributeur : Marie-Luce Taupin <>
Soumis le : mercredi 27 septembre 2006 - 10:25:57
Dernière modification le : jeudi 31 mai 2018 - 09:12:01
Document(s) archivé(s) le : lundi 5 avril 2010 - 23:13:06

### Citation

Fabienne Comte, Jérôme Dedecker, Marie-Luce Taupin. Adaptive density estimation for general ARCH models. 2006. 〈hal-00101417〉

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