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Bayesian model selection and prediction with empirical applications

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  • Phillips, Peter C. B.

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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  • Phillips, Peter C. B., 1995. "Bayesian model selection and prediction with empirical applications," Journal of Econometrics, Elsevier, vol. 69(1), pages 289-331, September.
    • Handle: RePEc:eee:econom:v:69:y:1995:i:1:p:289-331
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    1. 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.
    2. 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.
    3. Yock Y. Chong & David F. Hendry, 1986. "Econometric Evaluation of Linear Macro-Economic Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(4), pages 671-690.
    4. 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.
    5. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
    6. 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.
    7. Phillips, Peter C.B., 1995. "Spurious Regression in Forecast-Encompassing Tests," Econometric Theory, Cambridge University Press, vol. 11(05), pages 1188-1190, October.
    8. 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..
    9. Min, Chung-ki & Zellner, Arnold, 1993. "Bayesian and non-Bayesian methods for combining models and forecasts with applications to forecasting international growth rates," Journal of Econometrics, Elsevier, vol. 56(1-2), pages 89-118, March.
    10. 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.
    11. 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.
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    Cited by:

    1. 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.
    2. Phillips, Peter C.B., 2005. "Automated Discovery In Econometrics," Econometric Theory, Cambridge University Press, vol. 21(1), pages 3-20, February.
    3. Kelvin Balcombe & Alastair Bailey & Iain Fraser, 2005. "Measuring the impact of R&D on Productivity from a Econometric Time Series Perspective," Journal of Productivity Analysis, Springer, vol. 24(1), pages 49-72, September.
    4. Tao Zeng & Yong Li & Jun Yu, 2014. "Deviance Information Criterion for Comparing VAR Models," Advances in Econometrics, in: Essays in Honor of Peter C. B. Phillips, volume 33, pages 615-637, Emerald Group Publishing Limited.
    5. Fernandez, Carmen & Ley, Eduardo & Steel, Mark F. J., 2001. "Benchmark priors for Bayesian model averaging," Journal of Econometrics, Elsevier, vol. 100(2), pages 381-427, February.
    6. 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.
    7. Kelvin Balcombe & Iain Fraser & Abhijit Sharma, 2011. "Bayesian model averaging and identification of structural breaks in time series," Applied Economics, Taylor & Francis Journals, vol. 43(26), pages 3805-3818.
    8. Aaron Schiff & Peter Phillips, 2000. "Forecasting New Zealand's real GDP," New Zealand Economic Papers, Taylor & Francis Journals, vol. 34(2), pages 159-181.
    9. Corradi, Valentina & Swanson, Norman R. & Olivetti, Claudia, 2001. "Predictive ability with cointegrated variables," Journal of Econometrics, Elsevier, vol. 104(2), pages 315-358, September.
    10. 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.
    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. Kelvin Balcombe, 2005. "Model Selection Using Information Criteria and Genetic Algorithms," Computational Economics, Springer;Society for Computational Economics, vol. 25(3), pages 207-228, June.
    13. Abdulnasser Hatemi-J & Eduardo Roca, 2006. "Calculating the optimal hedge ratio: constant, time varying and the Kalman Filter approach," Applied Economics Letters, Taylor & Francis Journals, vol. 13(5), pages 293-299.
    14. 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.
    15. 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.
    16. Phillips, Peter C.B., 2003. "Vision And Influence In Econometrics: John Denis Sargan," Econometric Theory, Cambridge University Press, vol. 19(3), pages 495-511, June.
    17. Phillips, Peter C. B., 1998. "Impulse response and forecast error variance asymptotics in nonstationary VARs," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 21-56.
    18. Peter C. B. Phillips, 2003. "Laws and Limits of Econometrics," Economic Journal, Royal Economic Society, vol. 113(486), pages 26-52, March.
    19. 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.

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