Bayesian nonparametric estimation of the spectral density of a long memory Gaussian time series
| dc.creator | Rousseau, Judith | |
| dc.creator | Liseo, Brunero | |
| dc.date | 2007-11-06 | |
| dc.date.accessioned | 2026-07-07T08:41:00Z | |
| dc.date.available | 2026-07-07T08:41:00Z | |
| dc.description | Let $\mathbf {X}=\{X_t, t=1,2,... \}$ be a stationary Gaussian random process, with mean $EX_t=μ$ and covariance function $γ(τ)=E(X_t-μ)(X_{t+τ}-μ)$. Let $f(λ)$ be the corresponding spectral density; a stationary Gaussian process is said to be long-range dependent, if the spectral density $f(λ)$ can be written as the product of a slowly varying function $\tilde{f}(λ)$ and the quantity $λ^{-2d}$. In this paper we propose a novel Bayesian nonparametric approach to the estimation of the spectral density of $\mathbf {X}$. We prove that, under some specific assumptions on the prior distribution, our approach assures posterior consistency both when $f(\cdot)$ and $d$ are the objects of interest. The rate of convergence of the posterior sequence depends in a significant way on the structure of the prior; we provide some general results and also consider the fractionally exponential (FEXP) family of priors (see below). Since it has not a well founded justification in the long memory set-up, we avoid using the Whittle approximation to the likelihood function and prefer to use the true Gaussian likelihood. | |
| dc.description | Submitted to the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/0711.0876 | |
| dc.identifier | http://arxiv.org/abs/0711.0876 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/141543 | |
| dc.subject | Statistics Theory | |
| dc.subject | 62G20 (Primary); 62M15 (Secondary) | |
| dc.title | Bayesian nonparametric estimation of the spectral density of a long memory Gaussian time series | |
| dc.type | text |