Graphical techniques for selecting explanatory variables for time series data

Bayesian model building techniques are developed for data with a strong time series structure and possibly exogenous explanatory variables that have strong explanatory and predictive power. The emphasis is on finding whether there are any explanatory variables that might be used for modelling if the data have a strong time series structure that should also be included. We use a time series model that is linear in past observations and that can capture both stochastic and deterministic trend, seasonality and serial correlation. We propose the plotting of absolute predictive error against predictive standard deviation. A series of such plots is utilized to determine which of several nested and non-nested models is optimal in terms of minimizing the dispersion of the predictive distribution and restricting predictive outliers. We apply the techniques to modelling monthly counts of fatal road crashes in Australia where economic, consumption and weather variables are available and we find that three such variables should be included in addition to the time series filter. The approach leads to graphical techniques to determine strengths of relationships between the dependent variable and covariates and to detect model inadequacy as well as determining useful numerical summaries.