GRAPHICAL TECHNIQUES FOR SELECTING EXPLANATORY VARIABLES FOR TIME-SERIES DATA

Bayesian model building techniques are developed for data with a stron g time series structure and possibly exogenous explanatory variables t hat have strong explanatory and predictive power. The emphasis is on f inding whether there are any explanatory variables that might be used for modelling if the data have a strong time series structure that sho uld also be included. We use a time series model that is linear in pas t 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 ser ies 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 a pply the techniques to modelling monthly counts of fatal road crashes in Australia where economic, consumption and weather variables are ava ilable and we find that three such variables should be included in add ition to the time series filter. The approach leads to graphical techn iques to determine strengths of relationships between the dependent va riable and covariates and to detect model inadequacy as well as determ ining useful numerical summaries.