New approaches to prior specification and structuring in autoregressive time series models are introduced and developed. We focus on defining classes of prior distributions for parameters and latent variables related to latent components of an autoregressive model for an observed time series. These new priors naturally permit the incorporation of both qualitative and quantitative prior information about the number and relative importance of physically meaningful components that represent low frequency trends, quasi-periodic sub-processes, and high frequency residual noise components of observed series. The class of priors also naturally incorporates uncertainty about model order, and hence leads in posterior analysis to model order assessment and resulting posterior and predictive inferences that incorporate full uncertainties about model order as well as model parameters. Analysis also formally incorporates uncertainty, and leads to inferences about, unknown initial values of the time series, as it does for predictions of future values. Posterior analysis involves easily implemented iterative simulation methods, developed and described here.

One motivating applied field is climatology, where the evaluation of latent structure, especially quasi-periodic structure, is of critical importance in connection with issues of global climatic variability. We explore analysis of data from the Southern Oscillation Index (SOI), one of several series that has been central in recent high-profile debates in the atmospheric sciences about recent apparent trends in climatic indicators.

This research was partially supported by the National Science Foundation uder grants DMS-9704432 and DMS-9707914.

This paper is to appear in the Journal of the Royal Statistical Society (Series B) in 1999

The manuscript is available in either postscript or pdf