UC Santa Cruz

We introduce a novel Bayesian modeling approach to spectral density estimation for multiple time series. Considering first the case of non-stationary time

series, the log-periodogram of 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 log-spectral

density, we develop a hierarchical extension for multiple stationary time series.

Specifically, we set the mean functions to be common to all log-spectral densities and model time series specific mixtures 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. We then

extend the model to multiple locally stationary time series, a particular class of non-stationary time series, making it suitable for the analysis of time series with spectral characteristics that vary slowly with time. The modeling

approach is illustrated with different types of simulated datasets, and used for

spectral analysis of multichannel electroencephalographic recordings (EEGs),

which provides a key motivating application for the proposed methodology.