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

Judith Rousseau (1, 2) , Nicolas Chopin (1) , Brunero Liseo (3)

1 CREST - Centre de Recherche en Économie et Statistique
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
3 UNIROMA - Università degli Studi di Roma "La Sapienza" = Sapienza University [Rome]

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

Mots clés: Bayesian nonparametric; consistency; FEXP priors; Gaussian long memory processes; rates of convergence

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Judith Rousseau, Nicolas Chopin, Brunero Liseo. Bayesian nonparametric estimation of the spectral density of a long or intermediate memory Gaussian process. Annals of Statistics, 2012, 40 (2), pp.964-995. ⟨10.1214/11-AOS955SUPP⟩. ⟨hal-00504969⟩