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A Bayesian Analysis Of The Unit Root Hypothesis

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  • Schotman, P.
  • van Dijk, H. K.

Abstract

We propose a posterior odds analysis in order to compare a random walk model with a first-order stationary autoregressive model. We will study in detail the effect of the presence of a constant term representing an unknown mean of the series. Since the unconditional mean is not identifiable under the random walk hypothesis, one must be careful in specifying a reasonable prior for this model. The sampling properties of the posterior odds statistic are compared with such classical test statistics as proposed by Fuller [1976], and by Bhargava [1986]. The results indicate that the posterior odds compare favorably with these classical tests. Empirical results on time series of real exchange rates indicate that a Bayesian analysis can lead to different conclusions concerning the random walk behaviour of real exchange rates.

Suggested Citation

  • Schotman, P. & van Dijk, H. K., 1989. "A Bayesian Analysis Of The Unit Root Hypothesis," Econometric Institute Archives 272385, Erasmus University Rotterdam.
    • Handle: RePEc:ags:eureia:272385
    DOI: 10.22004/ag.econ.272385
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    References listed on IDEAS

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    1. Sims, Christopher A., 1988. "Bayesian skepticism on unit root econometrics," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 463-474.
    2. Huizinga, John, 1987. "An empirical investigation of the long-run behavior of real exchange rates," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 27(1), pages 149-214, January.
    3. Jeffrey A. Frankel & Richard Meese, 1987. "Are Exchange Rates Excessively Variable?," NBER Chapters, in: NBER Macroeconomics Annual 1987, Volume 2, pages 117-162, National Bureau of Economic Research, Inc.
    4. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-1072, June.
    5. Evans, G B A & Savin, N E, 1984. "Testing for Unit Roots: 2," Econometrica, Econometric Society, vol. 52(5), pages 1241-1269, September.
    6. Cochrane, John H, 1988. "How Big Is the Random Walk in GNP?," Journal of Political Economy, University of Chicago Press, vol. 96(5), pages 893-920, October.
    7. Spanos,Aris, 1986. "Statistical Foundations of Econometric Modelling," Cambridge Books, Cambridge University Press, number 9780521269124, November.
    8. Alok Bhargava, 1986. "On the Theory of Testing for Unit Roots in Observed Time Series," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(3), pages 369-384.
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    Cited by:

    1. Stock, James H., 1991. "Confidence intervals for the largest autoregressive root in U.S. macroeconomic time series," Journal of Monetary Economics, Elsevier, vol. 28(3), pages 435-459, December.

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