Applied Bayesian Modelling, 2nd Edition

Chapter 6Models for time series

6.1 Introduction

Many scientific disciplines raise issues in representing and forecasting series of observations generated in time. Often the series, although varying continuously in time, is observed at discrete time points, . Bayesian perspectives are relevant since increasingly time series models are framed hierarchically in terms of hyperparameters and latent state variables, both conditional on the observations. Recent overviews of time series modelling with a Bayesian perspective include Prado and West (2010), Steel (2008), Migon et al. (2005), Johannes and Polson (2009), De Pooter et al. (2006) and Geweke and Whiteman (2006). General time series computing options in R are discussed by McLeod et al. (2012), while specifically Bayesian packages for time series models (possibly only for certain model classes) include BUGS, R-INLA, tsbugs, stochvol, BayesGARCH, MSBVAR and dlm.

The goals of time series models include smoothing an irregular series, forecasting series into the medium or long-term future, and causal modelling of variables moving in parallel through time. Time series analysis exploits the temporal dependencies both in the deterministic (regression) and stochastic (error) components of the model. In fact dynamic regression models are defined when model components are indexed by time, and a lag appears on one or more of them in the ...