Bayes Models and Forecasts of Australian Macroeconomic Time Series

This paper provides an empirical implementation of some recent work by the author and Werner Ploberger on the development of “Bayes models” for time series. The methods offer a new data-based approach to model selection, to hypothesis testing and to forecast evaluation in the analysis of time series. A particular advantage of the approach is that modelling issues such as lag order, parameter constancy, and the presence of deterministic and stochastic trends all come within the compass of the same statistical methodology, as do the evaluation of forecasts from competing models. The paper shows how to build parsimonious empirical “Bayes models” using the new approach and applies the methodology to some Australian macroeconomic data. “Bayes models” are constructed for 13 quarterly Australian macroeconomic time series over the period 1959(3)-1987(4). These models are compared with certain fixed format models (like an AR(4) + linear trend) in terms of their forecasting performance over the period 1988(1)-1991(4). The “Bayes models” are found to be superior in these forecasting exercises for 10 of the 13 series, while at the same time being more parsimonious in form.