BAYESIAN MODEL SELECTION AND PREDICTION WITH EMPIRICAL APPLICATIONS

This paper builds on some recent work by the author and Werner Ploberg er (1991, 1994) on the development of 'Bayes models' for time series a nd on the authors' model selection criterion 'PIC', The PIC criterion is used in this paper to determine the lag order, the trend degree, an d the presence or absence of a unit root in an autoregression with det erministic trend. A new forecast-encompassing test for Bayes models is developed which allows one Bayes model to be compared with another on the basis of their respective forecasting performance. The paper repo rts an extended empirical application of the methodology to the Nelson -Plosser (1982) and Schotman-van Dijk (1991) data. It is shown that pa rsimonious evolving-format Bayes models forecast-encompass fixed Bayes models of the 'AR(3) + linear trend' variety for most of these series . In some cases, the forecast performance of the parsimonious Bayes mo dels is substantially superior, The results cast some doubts on the va lue of working with fixed-format time series models in empirical resea rch and demonstrate the practical advantages of evolving-format models , The paper makes a new suggestion for modelling interest rates in ter ms of reciprocals of levels rather than levels (which display more vol atility) and shows that the best data-determined model for this transf ormed series is a martingale.