Bayesian multiscale feature detection of log-spectral densities
A fully-automatic Bayesian visualization tool to identify periodic components of evenly sampled stationary time series, is presented. The given method applies the multiscale ideas of the SiZer-methodology to the log-spectral density of a given series. The idea is to detect significant peaks in the true underlying curve viewed at different resolutions or scales. The results are displayed in significance maps, illustrating for which scales and for which frequencies, peaks in the log-spectral density are detected as significant. The inference involved in producing the significance maps is performed using the recently developed simplified Laplace approximation. This is a Bayesian deterministic approach used to get accurate estimates of posterior marginals for latent Gaussian Markov random fields at a low computational cost, avoiding the use of Markov chain Monte Carlo techniques. Application of the given exploratory tool is illustrated analyzing both synthetic and real time series.
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- Hannig, J. & Marron, J.S., 2006. "Advanced Distribution Theory for SiZer," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 484-499, June.
- Håvard Rue & Sara Martino & Nicolas Chopin, 2009. "Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 319-392.
- Nidhan Choudhuri & Subhashis Ghosal & Anindya Roy, 2004. "Bayesian Estimation of the Spectral Density of a Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1050-1059, December.
- Oigard, Tor Arne & Rue, Havard & Godtliebsen, Fred, 2006. "Bayesian multiscale analysis for time series data," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1719-1730, December.
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