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Bayesian Model Selection and Prediction with Empirical Applications

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Abstract

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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File URL: http://cowles.econ.yale.edu/P/cd/d10a/d1023.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1023.

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Length: 31 pages
Date of creation: Jul 1992
Date of revision:
Publication status: Published in Journal of Econometrics (1995), 69: 289-331
Handle: RePEc:cwl:cwldpp:1023

Note: CFP 911.
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References

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  1. 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.
  2. 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.
  3. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
  4. Phillips, Peter C.B., 1995. "Spurious Regression in Forecast-Encompassing Tests," Econometric Theory, Cambridge University Press, vol. 11(05), pages 1188-1190, October.
  5. 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.
  6. 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.
  7. 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.
  8. Min, C.K. & Zellner, A., 1992. ""Bayesian and Non-Bayesian Methods for Combining Models and Forecasts with Applications to Forecasting International Growth Rates"," Papers 90-92-23, California Irvine - School of Social Sciences.
  9. 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.
  10. 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.
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Citations

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Cited by:
  1. 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.
  2. Peter C.B. Phillips, 1995. "Impulse Response and Forecast Error Variance Asymptotics in Nonstationary VAR's," Cowles Foundation Discussion Papers 1102, Cowles Foundation for Research in Economics, Yale University.
  3. Phillips, Peter C.B., 2003. "Vision And Influence In Econometrics: John Denis Sargan," Econometric Theory, Cambridge University Press, vol. 19(03), pages 495-511, June.
  4. Carmen Fernandez & E Ley & Mark F J Steel, 2004. "Benchmark priors for Bayesian models averaging," ESE Discussion Papers 66, Edinburgh School of Economics, University of Edinburgh.
  5. Aaron F. Schiff & Peter C.B. Phillips, 2000. "Forecasting New Zealand's Real GDP," Cowles Foundation Discussion Papers 1278, Cowles Foundation for Research in Economics, Yale University.
  6. Clark, Todd E. & McCracken, Michael W., 2005. "The power of tests of predictive ability in the presence of structural breaks," Journal of Econometrics, Elsevier, vol. 124(1), pages 1-31, January.
  7. Peter C. B. Phillips, 2003. "Laws and Limits of Econometrics," Economic Journal, Royal Economic Society, vol. 113(486), pages C26-C52, March.
  8. Kelvin Balcombe, 2005. "Model Selection Using Information Criteria and Genetic Algorithms," Computational Economics, Society for Computational Economics, vol. 25(3), pages 207-228, June.
  9. Allen, P. Geoffrey & Morzuch, Bernard J., 2006. "Twenty-five years of progress, problems, and conflicting evidence in econometric forecasting. What about the next 25 years?," International Journal of Forecasting, Elsevier, vol. 22(3), pages 475-492.
  10. Qi, Min & Zhang, Guoqiang Peter, 2001. "An investigation of model selection criteria for neural network time series forecasting," European Journal of Operational Research, Elsevier, vol. 132(3), pages 666-680, August.
  11. Peter C.B. Phillips, 1995. "Automated Forecasts of Asia-Pacific Economic Activity," Cowles Foundation Discussion Papers 1103, Cowles Foundation for Research in Economics, Yale University.
  12. Peter C.B. Phillips, 1992. "Bayes Models and Forecasts of Australian Macroeconomic Time Series," Cowles Foundation Discussion Papers 1024, Cowles Foundation for Research in Economics, Yale University.
  13. Peter C.B. Phillips, 2004. "Automated Discovery in Econometrics," Cowles Foundation Discussion Papers 1469, Cowles Foundation for Research in Economics, Yale University.
  14. Peter C.B. Phillips, 1992. "Bayes Methods for Trending Multiple Time Series with an Empirical Application to the US Economy," Cowles Foundation Discussion Papers 1025, Cowles Foundation for Research in Economics, Yale University.
  15. Corradi, Valentina & Swanson, Norman R. & Olivetti, Claudia, 2001. "Predictive ability with cointegrated variables," Journal of Econometrics, Elsevier, vol. 104(2), pages 315-358, September.

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