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.