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Adaptive Density Estimation For General Arch Models

Author

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

Abstract

We consider a model Yt = σtηt in which (σt) is not independent of the noise process (ηt) but σt is independent of ηt for each t. We assume that (σt) is stationary, and we propose an adaptive estimator of the density of ln(σt2) based on the observations Yt. Under a new dependence structure, the τ-dependency defined by Dedecker and Prieur (2005, Probability Theory and Related Fields 132, 203–236), 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 (σt) and (ηt) 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.

Suggested Citation

  • Comte, F. & Dedecker, J. & Taupin, M.L., 2008. "Adaptive Density Estimation For General Arch Models," Econometric Theory, Cambridge University Press, vol. 24(6), pages 1628-1662, December.
    • Handle: RePEc:cup:etheor:v:24:y:2008:i:06:p:1628-1662_08
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    Cited by:

    1. Van Es, Bert & Spreij, Peter, 2011. "Estimation of a multivariate stochastic volatility density by kernel deconvolution," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 683-697, March.
    2. Delaigle, Aurore & Meister, Alexander & Rombouts, Jeroen, 2016. "Root-T consistent density estimation in GARCH models," Journal of Econometrics, Elsevier, vol. 192(1), pages 55-63.

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