# 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.
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https://hal.archives-ouvertes.fr/hal-00101417
Contributor : Marie-Luce Taupin <>
Submitted on : Wednesday, September 27, 2006 - 10:25:57 AM
Last modification on : Monday, December 23, 2019 - 3:50:10 PM
Long-term archiving on: Monday, April 5, 2010 - 11:13:06 PM

### Citation

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

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