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- W1807453861 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." @default.
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- W1807453861 date "2012-04-01" @default.
- W1807453861 modified "2023-10-13" @default.
- W1807453861 title "Bayesian nonparametric estimation of the spectral density of a long or intermediate memory Gaussian process" @default.
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- W1807453861 doi "https://doi.org/10.1214/11-aos955" @default.
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