Priors and Component Structures in Autoregressive Time Series Models

Abstract

Summary: 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 subprocesses 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 field of application 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 the analysis of data from the southern oscillation index, one of several series that has been central in recent high profile debates in the atmospheric sciences about recent apparent trends in climatic indicators.