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April 2012 Bayesian nonparametric estimation of the spectral density of a long or intermediate memory Gaussian process
Judith Rousseau, Nicolas Chopin, Brunero Liseo
Ann. Statist. 40(2): 964-995 (April 2012). DOI: 10.1214/11-AOS955

Abstract

A stationary Gaussian process is said to be long-range dependent (resp., anti-persistent) if its spectral density $f(\lambda)$ can be written as $f(\lambda)=|\lambda|^{-2d}g(|\lambda|)$, where $0<d<1/2$ (resp., $-1/2<d<0$), and $g$ is continuous and positive. We propose a novel Bayesian nonparametric approach for the estimation of the spectral density of such processes. We prove posterior consistency for both $d$ and $g$, under appropriate conditions on the prior distribution. We establish the rate of convergence for a general class of priors and apply our results to the family of fractionally exponential priors. Our approach is based on the true likelihood and does not resort to Whittle’s approximation.

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Judith Rousseau. Nicolas Chopin. Brunero Liseo. "Bayesian nonparametric estimation of the spectral density of a long or intermediate memory Gaussian process." Ann. Statist. 40 (2) 964 - 995, April 2012. https://doi.org/10.1214/11-AOS955

Information

Published: April 2012
First available in Project Euclid: 18 July 2012

zbMATH: 1274.62340
MathSciNet: MR2985940
Digital Object Identifier: 10.1214/11-AOS955

Subjects:
Primary: 62G20
Secondary: 62M15

Keywords: Bayesian nonparametric , consistency , FEXP priors , Gaussian long memory processes , rates of convergence

Rights: Copyright © 2012 Institute of Mathematical Statistics

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Vol.40 • No. 2 • April 2012
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