ADAPTIVE DENSITY ESTIMATION FOR GENERAL ARCH MODELS

F. Comte, J. Dedecker and M.L. Taupin

Econometric Theory, 2008, vol. 24, issue 06, pages 1628-1662

Abstract: We consider a model Yt = t in which ( t) but t for each t. We assume that ( t2) based on the observations Yt. Under a new dependence structure, the 236), we prove that the rates of this nonparametric estimator coincide with the rates obtained in the independent and identically distributed (i.i.d.) case when ( t) are independent. The results apply to various linear and nonlinear general autoregressive conditionally heteroskedastic (ARCH) processes. They are illustrated by simulations applying the deconvolution algorithm of Comte, Rozenholc, and Taupin (2006, Canadian Journal of Statistics 34, 431 452) to a new noise density.

Date: 2008

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