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Testing for Multiple Bubbles

  • Peter C.B. Phillips

    ()

    (Yale University, University of Auckland, University of Southampton & Singapore Management University)

  • Shu-Ping Shi

    ()

    (Research School of Economics, The Australian National University)

  • Jun Yu

    ()

    (School of Economics, Singapore Management Unversity)

Identifying explosive bubbles that are characterized by periodically collapsing behavior over time has been a major concern in the literature and is of great importance for practitioners. The complexity of the nonlinear structure in multiple bubble phenomena diminishes the discriminatory power of existing tests, as evidenced in early simulations conducted by Evans (1991). Multiple collapsing bubble episodes within the same sample period make bubble diagnosis particularly di¢ cult and complicate attempts at econometric dating. The present paper systematically investigates these issues and develops new procedures for practical implementation and surveillance strategies by central banks. We show how the testing procedure and dating algorithm of Phillips, Wu and Yu (2011, PWY) is affected by multiple bubbles and may fail to be consistent. To assist performance in such contexts, the present paper proposes a generalized version of the sup ADF test of PWY that addresses the difficulty. The asymptotic distribution of the generalized test is provided and the test is shown to signfi cantly improve discriminatory power in simulations. The paper advances a new date-stamping strategy for the origination and termination of multiple bubbles that is based on this generalized test and consistency of the date-stamping algorithm is established. The new strategy leads to distinct power gains over the date-stamping strategy of PWY when multiple bubbles occur. Empirical applications are conducted with both tests along with their respective date-stamping technology to S&P 500 stock market data from January 1871 to December 2010. The new approach identi es many key historical episodes of exuberance and collapse over this period, whereas the strategy of PWY locates only two such episodes in the same sample range.

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Paper provided by Singapore Management University, School of Economics in its series Working Papers with number 09-2011.

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Length: 67 pages
Date of creation: Aug 2011
Date of revision:
Publication status: Published in SMU Economics and Statistics Working Paper Series
Handle: RePEc:siu:wpaper:09-2011
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  1. Busetti, Fabio & Taylor, A. M. Robert, 2004. "Tests of stationarity against a change in persistence," Journal of Econometrics, Elsevier, vol. 123(1), pages 33-66, November.
  2. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
  3. Campbell, J.Y. & Perron, P., 1991. "Pitfalls and Opportunities: What Macroeconomics should know about unit roots," Papers 360, Princeton, Department of Economics - Econometric Research Program.
  4. Peter C. B. Phillips & Jun Yu, 2009. "Dating the Timeline of Financial Bubbles During the Subprime Crisis," Working Papers 18-2009, Singapore Management University, School of Economics.
  5. Phillips, Peter C.B. & Magdalinos, Tassos, 2007. "Limit theory for moderate deviations from a unit root," Journal of Econometrics, Elsevier, vol. 136(1), pages 115-130, January.
  6. Pietro Veronesi & Lubos Pastor, 2005. "Was There a Nasdaq Bubble in the Late 1990s?," 2005 Meeting Papers 95, Society for Economic Dynamics.
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  8. Bhargava, Alok, 1986. "On the Theory of Testing for Unit Roots in Observed Time Series," Review of Economic Studies, Wiley Blackwell, vol. 53(3), pages 369-84, July.
  9. Peter C.B. Philips & Yangru Wu & Jun Yu, 2009. "Explosive Behavior in the 1990s Nasdaq : When Did Exuberance Escalate Asset Values?," Finance Working Papers 23050, East Asian Bureau of Economic Research.
  10. 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.
  11. Refet S. Gürkaynak, 2008. "Econometric Tests Of Asset Price Bubbles: Taking Stock ," Journal of Economic Surveys, Wiley Blackwell, vol. 22(1), pages 166-186, 02.
  12. M. Funke & S. Hall & M. Solá, 1993. "Rational bubbles during Polland’s hiperinflation: implications and empirical evidence," Documentos de Trabajo (working papers) 1193, Department of Economics - dECON.
  13. 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.
  14. Kim, Jae-Young, 2000. "Detection of change in persistence of a linear time series," Journal of Econometrics, Elsevier, vol. 95(1), pages 97-116, March.
  15. Diba, Behzad T & Grossman, Herschel I, 1988. "Explosive Rational Bubbles in Stock Prices?," American Economic Review, American Economic Association, vol. 78(3), pages 520-30, June.
  16. Ulrich Homm & Jörg Breitung, 2010. "Testing for Speculative Bubbles in Stock Markets: A Comparison of Alternative Methods," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 10(1), pages 198-231, 2012 10 1.
  17. 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.
  18. van Norden Simon & Vigfusson Robert, 1998. "Avoiding the Pitfalls: Can Regime-Switching Tests Reliably Detect Bubbles?," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 3(1), pages 1-24, April.
  19. Chu, Chia-Shang James & Stinchcombe, Maxwell & White, Halbert, 1996. "Monitoring Structural Change," Econometrica, Econometric Society, vol. 64(5), pages 1045-65, September.
  20. 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.
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