ABSTRACT
This chapter provides an introduction to the analysis of time series using autoregressive models. It discusses Non-Gaussian time series and explores Forecasting of time series. integrated nested Laplace approximation provides a number of options to model data collected in space and time. E. T. Krainski et al. provides examples on space-time models for geostatistical data and point patterns. When time is indexed over a discrete domain autoregressive models are a convenient way to model the data. Time series forecasting in Bayesian inference can be regarded as fitting a model with some missing observations in the response, which requires computing the predictive distribution at future times. If the model being fit includes covariates these must also be available as well for the years to be predicted. A spatio-temporal model is said to be separable when the space-time covariance structure can be decomposed as a spatial and a temporal term.
