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Bayesian Inference for a Threshold Autoregression with a Unit Root

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  • Penelope Smith

    (Melbourne Institute of Applied Economic and Social Research, The University of Melbourne)

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    Abstract

    A Bayesian approach to distinguishing between nonlinear and unit root behavior offers several practical advantages over equivalent frequentist procedures. Foremost among these advantages is the simplicity of the test. This paper compares the small sample power and size properties of a joint Bayesian test for a unit root and a threshold effect with Caner and Hansen's (2001) frequentist strategy. The results from Monte Carlo experiments indicate that the simpler Bayesian test performs at least as well as Caner and Hansen's procedure.

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    File URL: http://www.melbourneinstitute.com/downloads/working_paper_series/wp2006n20.pdf
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    Bibliographic Info

    Paper provided by Melbourne Institute of Applied Economic and Social Research, The University of Melbourne in its series Melbourne Institute Working Paper Series with number wp2006n20.

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    Length: 40 pages
    Date of creation: Oct 2006
    Date of revision:
    Handle: RePEc:iae:iaewps:wp2006n20

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    Postal: Melbourne Institute of Applied Economic and Social Research, The University of Melbourne, Victoria 3010 Australia
    Phone: +61 3 8344 2100
    Fax: +61 3 8344 2111
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    Web page: http://www.melbourneinstitute.com/
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    1. Andrews, Donald W K, 1994. "The Large Sample Correspondence between Classical Hypothesis Tests and Bayesian Posterior Odds Tests," Econometrica, Econometric Society, vol. 62(5), pages 1207-32, September.
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    4. Basci Erdem & Caner Mehmet, 2005. "Are Real Exchange Rates Nonlinear or Nonstationary? Evidence from a New Threshold Unit Root Test," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 9(4), pages 1-21, December.
    5. Robert B. Davies, 2002. "Hypothesis testing when a nuisance parameter is present only under the alternative: Linear model case," Biometrika, Biometrika Trust, vol. 89(2), pages 484-489, June.
    6. 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.
    7. Hansen, B.E., 1991. "Inference when a Nuisance Parameter is Not Identified Under the Null Hypothesis," RCER Working Papers 296, University of Rochester - Center for Economic Research (RCER).
    8. Koop, Gary & Potter, Simon M., 1998. "Bayes factors and nonlinearity: Evidence from economic time series1," Journal of Econometrics, Elsevier, vol. 88(2), pages 251-281, November.
    9. Mehmet Caner & Bruce E. Hansen, 2001. "Threshold Autoregression with a Unit Root," Econometrica, Econometric Society, vol. 69(6), pages 1555-1596, November.
    10. 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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    12. Christopher A. Sims, 1988. "Bayesian skepticism on unit root econometrics," Discussion Paper / Institute for Empirical Macroeconomics 3, Federal Reserve Bank of Minneapolis.
    13. Frédérique BEC & Mélika BEN SALEM & Ronald MACDONALD, 2006. "Real exchange rates and real interest rates : a nonlinear perspective," Discussion Papers (REL - Recherches Economiques de Louvain) 2006024, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
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    16. Gary Koop & Simon M. Potter, 2004. "Dynamic asymmetries in US unemployment," ESE Discussion Papers 15, Edinburgh School of Economics, University of Edinburgh.
    17. Jae-Young Kim, 1998. "Large Sample Properties of Posterior Densities, Bayesian Information Criterion and the Likelihood Principle in Nonstationary Time Series Models," Econometrica, Econometric Society, vol. 66(2), pages 359-380, March.
    18. Donald W.K. Andrews & Werner Ploberger, 1992. "Optimal Tests When a Nuisance Parameter Is Present Only Under the Alternative," Cowles Foundation Discussion Papers 1015, Cowles Foundation for Research in Economics, Yale University.
    19. Kim, Jae-Young, 1994. "Bayesian Asymptotic Theory in a Time Series Model with a Possible Nonstationary Process," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 764-773, August.
    20. Pedro Gouveia & Paulo Rodrigues, 2004. "Threshold Cointegration and the PPP Hypothesis," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(1), pages 115-127.
    21. Henry, Olan T. & Shields, Kalvinder, 2004. "Is there a unit root in inflation?," Journal of Macroeconomics, Elsevier, vol. 26(3), pages 481-500, September.
    22. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
    23. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-36, July.
    24. Eric Zivot & Peter C.B. Phillips, 1991. "A Bayesian Analysis of Trend Determination in Economic Time Series," Cowles Foundation Discussion Papers 1002, Cowles Foundation for Research in Economics, Yale University.
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