Bayesian model selection and prediction with empirical applications
This paper builds on some recent work by the author and Werner Ploberger (1991, 1994) on the development of "Bayes models" for time series and on the authors' model selection criterion "PIC." The PIC criterion is used in this paper to determine the lag order, the trend degree, and the presence or absence of a unit root in an autoregression with deterministic 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 reports an extended empirical application of the methodology to the Nelson-Plosser (1982)/Schotman-van Dijk (1991) data. It is shown that parsimonious, 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 models is substantially superior. The results cast some doubts on the value of working with fixed format time series models in empirical research and demonstrate the practical advantages of evolving-format models. The paper makes a new suggestion for modelling interest rates in terms of reciprocals of levels rather than levels (which display more volatility) and shows that the best data-determined model for this transformed series is a martingale. Keywords: Bayes model, Bayes measure, BIC, forecast, forecast-encompass, model selection, PIC, unit root
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- DeJong, David N. & Whiteman, Charles H., 1991. "Reconsidering 'trends and random walks in macroeconomic time series'," Journal of Monetary Economics, Elsevier, vol. 28(2), pages 221-254, October.
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"Bayesian and non-Bayesian methods for combining models and forecasts with applications to forecasting international growth rates,"
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- Phillips, Peter C.B. & Ploberger, Werner, 1994. "Posterior Odds Testing for a Unit Root with Data-Based Model Selection," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 774-808, August.
- Peter C.B. Phillips & Werner Ploberger, 1992. "Posterior Odds Testing for a Unit Root with Data-Based Model Selection," Cowles Foundation Discussion Papers 1017, Cowles Foundation for Research in Economics, Yale University.
- Florens, Jean-Pierre & Larribeau, Sophie & Mouchart, Michel, 1994. "Bayesian Encompassing Tests of a Unit Root Hypothesis," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 747-763, August.
- Florens, J.P. & Mouchart, M. & Larribeau-Nori, S., 1992. "Bayesian Encompassing Tests of Unit Root Hypothesis," Papers 92.274, Toulouse - GREMAQ.
- Phillips, Peter C.B., 1995. "Spurious Regression in Forecast-Encompassing Tests," Econometric Theory, Cambridge University Press, vol. 11(05), pages 1188-1190, October.
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- Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
- Peter C.B. Phillips, 1985. "Understanding Spurious Regressions in Econometrics," Cowles Foundation Discussion Papers 757, Cowles Foundation for Research in Economics, Yale University.
- Durlauf, Steven N & Phillips, Peter C B, 1988. "Trends versus Random Walks in Time Series Analysis," Econometrica, Econometric Society, vol. 56(6), pages 1333-1354, November.
- Steven N. Durlauf & Peter C.B. Phillips, 1986. "Trends Versus Random Walks in Time Series Analysis," Cowles Foundation Discussion Papers 788, Cowles Foundation for Research in Economics, Yale University.
- Peter C.B. Phillips & Werner Ploberger, 1991. "Time Series Modelling with a Bayesian Frame of Reference: 1. Concepts and Illustrations," Cowles Foundation Discussion Papers 980, Cowles Foundation for Research in Economics, Yale University.
- Schotman, Peter C & van Dijk, Herman K, 1991. "On Bayesian Routes to Unit Roots," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 6(4), pages 387-401, Oct.-Dec..
- Peter C. Schotman & Herman K. van Dijk, 1991. "On Bayesian routes to unit roots," Discussion Paper / Institute for Empirical Macroeconomics 43, Federal Reserve Bank of Minneapolis.
- Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162. Full references (including those not matched with items on IDEAS)
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