IDEAS home Printed from https://ideas.repec.org/p/cwl/cwldpp/1023.html
   My bibliography  Save this paper

Bayesian Model Selection and Prediction with Empirical Applications

Author

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

Suggested Citation

  • Peter C.B. Phillips, 1992. "Bayesian Model Selection and Prediction with Empirical Applications," Cowles Foundation Discussion Papers 1023, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1023
    Note: CFP 911.
    as

    Download full text from publisher

    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d10/d1023.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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," Review of Economic Studies, Oxford University Press, 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. Florens, J.-P. & Larribeau, S. & Mouchart, M., 1994. "Bayesian encompassing tests of a unit root hypothesis," LIDAM Reprints CORE 1120, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    12. 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)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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.
    3. 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.
    4. Phillips, Peter C.B., 2005. "Automated Discovery In Econometrics," Econometric Theory, Cambridge University Press, vol. 21(1), pages 3-20, February.
    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. 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.
    7. Tao Zeng & Yong Li & Jun Yu, 2014. "Deviance Information Criterion for Comparing VAR Models," Advances in Econometrics, in: Yoosoon Chang & Thomas B. Fomby & Joon Y. Park (ed.), Essays in Honor of Peter C. B. Phillips, volume 33, pages 615-637, Emerald Publishing Ltd.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. Peter C. B. Phillips, 2003. "Laws and Limits of Econometrics," Economic Journal, Royal Economic Society, vol. 113(486), pages 26-52, March.
    13. Aaron Schiff & Peter Phillips, 2000. "Forecasting New Zealand's real GDP," New Zealand Economic Papers, Taylor & Francis Journals, vol. 34(2), pages 159-181.
    14. Corradi, Valentina & Swanson, Norman R. & Olivetti, Claudia, 2001. "Predictive ability with cointegrated variables," Journal of Econometrics, Elsevier, vol. 104(2), pages 315-358, September.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Magris Martin & Iosifidis Alexandros, 2021. "Approximate Bayes factors for unit root testing," Papers 2102.10048, arXiv.org, revised Feb 2021.
    2. Lawrence E. Raffalovich, 1994. "Detrending Time Series," Sociological Methods & Research, , vol. 22(4), pages 492-519, May.
    3. Peter C. B. Phillips & Zhijie Xiao, 1998. "A Primer on Unit Root Testing," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 423-470, December.
    4. Cribari-Neto, Francisco, 1996. "On time series econometrics," The Quarterly Review of Economics and Finance, Elsevier, vol. 36(Supplemen), pages 37-60.
    5. Entorf, Horst, 1997. "Random walks with drifts: Nonsense regression and spurious fixed-effect estimation," Journal of Econometrics, Elsevier, vol. 80(2), pages 287-296, October.
    6. Ernst, Matthew & Rodecker, Jared & Luvaga, Ebby & Alexander, Terence & Kliebenstein, James & MIRANOWSKI, JOHN A, 1999. "The Viability of Methane Production by Anaerobic Digestion on Iowa Swine Farms," ISU General Staff Papers 199910010700001329, Iowa State University, Department of Economics.
    7. Palaskas, Theodosios B. & Varangis, Panos N., 1991. "Is there excess co-movement of primary commodity prices? A co-integration test," Policy Research Working Paper Series 758, The World Bank.
    8. Olivier Darné & Amélie Charles, 2011. "Large shocks in U.S. macroeconomic time series: 1860-1988," Cliometrica, Journal of Historical Economics and Econometric History, Association Française de Cliométrie (AFC), vol. 5(1), pages 79-100, January.
    9. Phillips, Peter C. B., 2002. "New unit root asymptotics in the presence of deterministic trends," Journal of Econometrics, Elsevier, vol. 111(2), pages 323-353, December.
    10. Koop, Gary & Steel, Mark F J, 1994. "A Decision-Theoretic Analysis of the Unit-Root Hypothesis Using Mixtures of Elliptical Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(1), pages 95-107, January.
    11. Charles, Amélie & Darné, Olivier, 2012. "Trends and random walks in macroeconomic time series: A reappraisal," Journal of Macroeconomics, Elsevier, vol. 34(1), pages 167-180.
    12. Grassi, S. & Proietti, T., 2014. "Characterising economic trends by Bayesian stochastic model specification search," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 359-374.
    13. Loukia Meligkotsidou & Elias Tzavalis & Ioannis D. Vrontos, 2004. "A Bayesian Analysis of Unit Roots and Structural Breaks in the Level and the Error Variance of Autoregressive Models," Working Papers 514, Queen Mary University of London, School of Economics and Finance.
    14. de Pooter, M.D. & Ravazzolo, F. & Segers, R. & van Dijk, H.K., 2008. "Bayesian near-boundary analysis in basic macroeconomic time series models," Econometric Institute Research Papers EI 2008-13, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    15. Jürgen Wolters & Uwe Hassler, 2006. "Unit Root Testing," Springer Books, in: Olaf Hübler & Jachim Frohn (ed.), Modern Econometric Analysis, chapter 4, pages 41-56, Springer.
    16. John D. Levendis, 2018. "Time Series Econometrics," Springer Texts in Business and Economics, Springer, number 978-3-319-98282-3, September.
    17. 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.
    18. Otto, Glenn & Wirjanto, Tony, 1989. "National Savings and Domestic Investment in the Long Run: Some Time Series Evidence for the U.S. and Canada," Queen's Institute for Economic Research Discussion Papers 275218, Queen's University - Department of Economics.
    19. Patrick Marsh, "undated". "A Measure of Distance for the Unit Root Hypothesis," Discussion Papers 05/02, Department of Economics, University of York.
    20. Geweke, John, 1994. "Priors for Macroeconomic Time Series and Their Application," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 609-632, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cwl:cwldpp:1023. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://edirc.repec.org/data/cowleus.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Matthew Regan (email available below). General contact details of provider: https://edirc.repec.org/data/cowleus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.