  We present a method for the joint analysis of a panel of possibly
nonstationary time series. The approach is Bayesian and uses a
covariate-dependent infinite mixture model to incorporate multiple time series,
with mixture components parameterized by a time varying mean and log spectrum.
The mixture components are based on AdaptSPEC, a nonparametric model which
adaptively divides the time series into an unknown number of segments and
estimates the local log spectra by smoothing splines. We extend AdaptSPEC to
handle missing values, a common feature of time series which can cause
difficulties for nonparametric spectral methods. A second extension is to allow
for a time varying mean. Covariates, assumed to be time-independent, are
incorporated via the mixture weights using the logistic stick breaking process.
The model can estimate time varying means and spectra at observed and
unobserved covariate values, allowing for predictive inference. Estimation is
performed by Markov chain Monte Carlo (MCMC) methods, combining data
augmentation, reversible jump, and Riemann manifold Hamiltonian Monte Carlo
techniques. We evaluate the methodology using simulated data, and describe
applications to Australian rainfall data and measles incidence in the US.
Software implementing the method proposed in this paper is available in the R
package BayesSpec.
