fixed format models. For ten out of the thirteen series considered here the Bayes models not only improve on the forecasts of more richly parameterised models but also encompass those forecasts. In effect, the predictive distribution of the best Bayes model explains the forecasts delivered by the rival model. According to our Bayesian forecast-encompassing statistic and given the actual forecast history, the posterior odds favour the Bayes models, sometimes by a factor as high as 30:1, as in the case of the short-term interest rate series.
The models we have considered in this paper are scalar time series models. However, all of the ideas we have employed extend in a natural way to multivariate time series; the statistical theory for this extension will be provided in a subsequent paper. And we hope to conduct some empirical exercises with these multivariate methods on Australian macroeconomic data at a later date.
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