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Identifying Speculative Bubbles with an Infinite Hidden Markov Model

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  • Shu-Ping Shi

    (Australian National University, Australia)

  • Yong Song

    (University of Technology Sydney, Australia)

Abstract

This paper proposes an infinite hidden Markov model (iHMM) to detect, date stamp, and estimate speculative bubbles. Three features make this new approach attractive to practitioners. first, the iHMM is capable of capturing the nonlinear dynamics of different types of bubble behaviors as it allows an infinite number of regimes. Second, the implementation of this procedure is straightforward as the detection, dating, and estimation of bubbles are done simultaneously in a coherent Bayesian framework. Third, the iHMM, by assuming hierarchical structures, is parsimonious and superior in out-of-sample forecast. Two empirical applications are presented: one to the Argentinian money base, exchange rate, and consumer price from January 1983 to November 1989; and the other to the U.S. oil price from April 1983 to December 2010. We find prominent results, which have not been discovered by the existing finite hidden Markov model. Model comparison shows that the iHMM is strongly supported by the predictive likelihood.

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Bibliographic Info

Paper provided by The Rimini Centre for Economic Analysis in its series Working Paper Series with number 26_12.

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Date of creation: Jun 2012
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Handle: RePEc:rim:rimwps:26_12

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Keywords: speculative bubbles; infinite hidden Markov model; Dirichlet process;

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  1. Peter C.B.Phillips & Jun Yu, 2009. "Dating the Timeline of Financial Bubbles During the Subprime Crisis," Working Papers CoFie-07-2009, Sim Kee Boon Institute for Financial Economics.
  2. Geweke, John & Amisano, Gianni, 2008. "Comparing and evaluating Bayesian predictive distributions of assets returns," Working Paper Series 0969, European Central Bank.
  3. Shu-ping Shi & Vipin Arora, 2011. "An Application Of Models Of Speculative Behaviour To Oil Prices," CAMA Working Papers 2011-11, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
  4. Psaradakis, Zacharias & Sola, Martin & Spagnolo, Fabio, 2001. "A simple procedure for detecting periodically collapsing rational bubbles," Economics Letters, Elsevier, vol. 72(3), pages 317-323, September.
  5. M. Hashem Pesaran & Davide Pettenuzzo & Allan Timmermann, 2006. "Forecasting Time Series Subject to Multiple Structural Breaks," Review of Economic Studies, Oxford University Press, vol. 73(4), pages 1057-1084.
  6. Geweke, John, 2007. "Interpretation and inference in mixture models: Simple MCMC works," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3529-3550, April.
  7. Charemza, Wojciech W. & Deadman, Derek F., 1995. "Speculative bubbles with stochastic explosive roots: The failure of unit root testing," Journal of Empirical Finance, Elsevier, vol. 2(2), pages 153-163, June.
  8. Evans, George W, 1991. "Pitfalls in Testing for Explosive Bubbles in Asset Prices," American Economic Review, American Economic Association, vol. 81(4), pages 922-30, September.
  9. Geweke, John & Jiang, Yu, 2011. "Inference and prediction in a multiple-structural-break model," Journal of Econometrics, Elsevier, vol. 163(2), pages 172-185, August.
  10. Chib, Siddhartha, 1996. "Calculating posterior distributions and modal estimates in Markov mixture models," Journal of Econometrics, Elsevier, vol. 75(1), pages 79-97, November.
  11. Teh, Yee Whye & Jordan, Michael I. & Beal, Matthew J. & Blei, David M., 2006. "Hierarchical Dirichlet Processes," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1566-1581, December.
  12. Hall, Stephen G & Psaradakis, Zacharias & Sola, Martin, 1999. "Detecting Periodically Collapsing Bubbles: A Markov-Switching Unit Root Test," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(2), pages 143-54, March-Apr.
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