Adaptive Bayesian Estimation of a spectral density

Rousseau, Judith; Kruijer, Willem

Rousseau, Judith; Kruijer, Willem (2011), Adaptive Bayesian Estimation of a spectral density. https://basepub.dauphine.fr/handle/123456789/7619

Type

Document de travail / Working paper

External document link

http://hal.archives-ouvertes.fr/hal-00641485/fr/

Date

2011

Publisher

Université Paris-Dauphine

Published in

Paris

Metadata

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Author(s)

Rousseau, Judith
Kruijer, Willem

Abstract (EN)

Rousseau et al. [8] recently studied the asymptotic behavior of Bayesian estimators in the FEXP-model for spectral densities of Gaussian time-series. For the L2-norm on the log-spectral densities, they proved that the convergence rate is at least n 2 +1 (log n) 2 +2 2 +1 , > 1 2 being the Sobolev-regularity of the true spectral density fo. We will improve upon the logarithmic factor, and prove that given a prior only depending on s > 1 2 , we have adaptivity to any s.

Subjects / Keywords

FEXP-model; Bayesian non-parametric; rates of convergence; adaptive estimation; long-memory time-series

JEL

C11 - Bayesian Analysis: General