Bayesian nonparametric estimation of the spectral density of a long or intermediate memory Gaussian process

Rousseau, Judith; Chopin, Nicolas; Liseo, Brunero

dc.contributor.author	Rousseau, Judith
dc.contributor.author	Chopin, Nicolas
dc.contributor.author	Liseo, Brunero
dc.date.accessioned	2010-07-23T14:57:24Z
dc.date.available	2010-07-23T14:57:24Z
dc.date.issued	2012
dc.identifier.uri	https://basepub.dauphine.fr/handle/123456789/4659
dc.language.iso	en	en
dc.subject	rates of convergence	en
dc.subject	Gaussian long memory processes	en
dc.subject	FEXP priors	en
dc.subject	consistency	en
dc.subject	Bayesian nonparametric	en
dc.subject.ddc	519	en
dc.subject.classificationjel	C14	en
dc.subject.classificationjel	C11	en
dc.title	Bayesian nonparametric estimation of the spectral density of a long or intermediate memory Gaussian process	en
dc.type	Article accepté pour publication ou publié
dc.description.abstracten	A stationary Gaussian process is said to be long-range dependent (resp., anti-persistent) if its spectral density f(λ) can be written as f(λ)=\|λ\|−2dg(\|λ\|), 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.
dc.identifier.citationpages	33	en
dc.relation.isversionofjnlname	Annals of Statistics
dc.relation.isversionofjnlvol	40
dc.relation.isversionofjnlissue	2
dc.relation.isversionofjnldate	2012
dc.relation.isversionofjnlpages	964-995
dc.relation.isversionofdoi	http://dx.doi.org/10.1214/11-AOS955SUPP
dc.identifier.urlsite	http://hal.archives-ouvertes.fr/hal-00504969/fr/	en
dc.description.sponsorshipprivate	oui	en
dc.relation.isversionofjnlpublisher	Institute of Mathematical Statistics
dc.subject.ddclabel	Probabilités et mathématiques appliquées	en

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Bayesian nonparametric estimation of the spectral density of a long or intermediate memory Gaussian process

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