bsplinePsd-package {bsplinePsd}

Bayesian Nonparametric Spectral Density Estimation Using B-Spline Priors

Description

Implementation of a Metropolis-within-Gibbs MCMC algorithm to flexibly estimate the spectral density of a stationary time series. The algorithm updates a nonparametric B-spline prior using the Whittle likelihood to produce pseudo-posterior samples.

Details

The function gibbs_bspline is an implementation of the (serial version of the) MCMC algorithm presented in Edwards et al. (2018). This algorithm uses a nonparametric B-spline prior to estimate the spectral density of a stationary time series and can be considered a generalisation of the algorithm of Choudhuri et al. (2004), which used the Bernstein polynomial prior. A Dirichlet process prior is used to find the weights for the B-spline densities used in the finite mixture and a seperate and independent Dirichlet process prior used to place knots. The algorithm therefore allows for a data-driven choice of the number of knots/mixture components and their locations.

Author(s)

Matthew C. Edwards, Renate Meyer, Nelson Christensen

Maintainer: Matthew C. Edwards <[e-mail]>

References

Edwards, M. C., Meyer, R., and Christensen, N. (2018), Bayesian nonparametric spectral density estimation using B-spline priors, Statistics and Computing, <https://doi.org/10.1007/s11222-017-9796-9>.

Choudhuri, N., Ghosal, S., and Roy, A. (2004), Bayesian estimation of the spectral density of a time series, Journal of the American Statistical Association, 99(468):1050–1059.