Quotation Cadonna, Annalisa, Prado, Raquel, Kottas, Athanasios. 2019. Bayesian spectral modeling for multiple time series. Journal of the American Statistical Association.


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Abstract

We develop a novel Bayesian modeling approach to spectral density estimation for multiple time series. The log-periodogram distribution for each series is modeled as a mixture of Gaussian distributions with frequency-dependent weights and mean functions. The implied model for the log-spectral density is a mixture of linear mean functions with frequency-dependent weights. The mixture weights are built through successive differences of a logit-normal distribution function with frequency-dependent parameters. Building from the construction for a single spectral density, we develop a hierarchical extension for multiple time series. Specifically, we set the mean functions to be common to all spectral densities and make the weights specific to the time series through the parameters of the logit-normal distribution. In addition to accommodating flexible spectral density shapes, a practically important feature of the proposed formulation is that it allows for ready posterior simulation through a Gibbs sampler with closed form full conditional distributions for all model parameters. The modeling approach is illustrated with simulated datasets, and used for spectral analysis of multichannel electroencephalographic recordings (EEGs), which provides a key motivating application for the proposed methodology.

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Publication's profile

Status of publication Published
Affiliation WU
Type of publication Journal article
Journal Journal of the American Statistical Association
Citation Index SCI
WU Journalrating 2009 A
WU-Journal-Rating new FIN-A, VW-A, WH-A
Language English
Title Bayesian spectral modeling for multiple time series
Year 2019
Reviewed? Y
DOI http://dx.doi.org/10.1080/01621459.2018.1520114
Open Access N

Associations

People
Cadonna, Annalisa (Former researcher)
External
Kottas, Athanasios (University of California, Santa Cruz, United States/USA)
Prado, Raquel (University of California, Santa Cruz, United States/USA)
Organization
Institute for Statistics and Mathematics IN (Details)
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