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Bayesian Unit Root Testing: The Effect Of Choice Of Prior On Test Outcomes

  • Charley Xia and William Griffiths

A Monte Carlo experiment is used to examine the size and power properties of alternative Bayesian tests for unit roots. Four different prior distributions for the root that is potentially unity – a uniform prior and priors attributable to Jeffreys, Lubrano, and Berger and Yang – are used in conjunction with two testing procedures: a credible interval test and a Bayes factor test. Two extensions are also considered: a test based on model averaging with different priors and a test with a hierarchical prior for a hyperparameter. The tests are applied to both trending and non-trending series. Our results favor the use of a prior suggested by Lubrano. Outcomes from applying the tests to some Australian macroeconomic time series are presented.

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File URL: http://fbe.unimelb.edu.au/__data/assets/pdf_file/0007/784312/1152.pdf
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Paper provided by The University of Melbourne in its series Department of Economics - Working Papers Series with number 1152.

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Length: 36 pages
Date of creation: 2012
Date of revision:
Handle: RePEc:mlb:wpaper:1152
Contact details of provider: Postal: Department of Economics, The University of Melbourne, 4th Floor, FBE Building, Level 4, 111 Barry Street. Victoria, 3010, Australia
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  1. Mayadunne, Geetha & Evans, Merran & Inder, Brett, 1995. "An Empirical Investigation of Shock Persistence in Economic Time Series," The Economic Record, The Economic Society of Australia, vol. 71(213), pages 145-56, June.
  2. DeJong, David N, et al, 1992. "Integration versus Trend Stationarity in Time Series," Econometrica, Econometric Society, vol. 60(2), pages 423-33, March.
  3. Olivier J. Blanchard & Lawrence H. Summers, 1986. "Hysteresis and the European Unemployment Problem," NBER Chapters, in: NBER Macroeconomics Annual 1986, Volume 1, pages 15-90 National Bureau of Economic Research, Inc.
  4. Bauwens, Luc & Lubrano, Michel & Richard, Jean-Francois, 2000. "Bayesian Inference in Dynamic Econometric Models," OUP Catalogue, Oxford University Press, number 9780198773139, March.
  5. Koop, Gary, 1991. "Intertemporal Properties of Real Output: A Bayesian Analysis," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(3), pages 253-65, July.
  6. 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.
  7. PareshKumar Narayan & Russell Smyth, 2005. "Structural Breaks And Unit Roots In Australian Macroeconomic Time Series," Pacific Economic Review, Wiley Blackwell, vol. 10(4), pages 421-437, December.
  8. Zivot, Eric, 1994. "A Bayesian Analysis Of The Unit Root Hypothesis Within An Unobserved Components Model," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 552-578, August.
  9. 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.
  10. Olivier J. Blanchard & Lawrence H. Summers, 1986. "Hysteresis in Unemployment," NBER Working Papers 2035, National Bureau of Economic Research, Inc.
  11. Berger, James O. & Yang, Ruo-Yong, 1994. "Noninformative Priors and Bayesian Testing for the AR(1) Model," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 461-482, August.
  12. Peter C.B. Phillips, 1990. "To Criticize the Critics: An Objective Bayesian Analysis of Stochastic Trends," Cowles Foundation Discussion Papers 950, Cowles Foundation for Research in Economics, Yale University.
  13. Christopher A. Sims, 1988. "Bayesian skepticism on unit root econometrics," Discussion Paper / Institute for Empirical Macroeconomics 3, Federal Reserve Bank of Minneapolis.
  14. Schotman, Peter & van Dijk, Herman K., 1991. "A Bayesian analysis of the unit root in real exchange rates," Journal of Econometrics, Elsevier, vol. 49(1-2), pages 195-238.
  15. Lubrano, Michel, 1995. "Testing for unit roots in a Bayesian framework," Journal of Econometrics, Elsevier, vol. 69(1), pages 81-109, September.
  16. Uhlig, Harald, 1994. "On Jeffreys Prior when Using the Exact Likelihood Function," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 633-644, August.
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