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Testing for Multiple Bubbles

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  • 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)

Abstract

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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Bibliographic Info

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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Keywords: Date-stamping strategy; Generalized sup ADF test; Multiple bubbles; Rational bubble; Periodically collapsing bubbles; Sup ADF test;

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References

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  1. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
  2. 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.
  3. Chu, Chia-Shang James & Stinchcombe, Maxwell & White, Halbert, 1996. "Monitoring Structural Change," Econometrica, Econometric Society, vol. 64(5), pages 1045-65, September.
  4. Peter C. B. Phillips & Jun Yu, 2010. "Dating the Timeline of Financial Bubbles during the Subprime Crisis," Cowles Foundation Discussion Papers 1770, Cowles Foundation for Research in Economics, Yale University.
  5. Refet Gurkaynak, 2005. "Econometric Tests of Asset Price Bubbles: Taking Stock," Finance 0504008, EconWPA.
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  8. Pietro Veronesi & Lubos Pastor, 2005. "Was There a Nasdaq Bubble in the Late 1990s?," 2005 Meeting Papers 95, Society for Economic Dynamics.
  9. Peter C. B. Phillips & Yangru Wu & Jun Yu, 2007. "Explosive Behavior in the 1990s Nasdaq: When Did Exuberance Escalate Asset Values?," Working Papers 222007, Hong Kong Institute for Monetary Research.
  10. 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.
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  12. 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.
  13. 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.
  14. 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.
  15. 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.
  16. 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.
  17. 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.
  18. 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.
  19. 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.
  20. 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.
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Citations

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Cited by:
  1. Bohl, Martin T. & Kaufmann, Philipp & Stephan, Patrick M., 2013. "From hero to zero: Evidence of performance reversal and speculative bubbles in German renewable energy stocks," Energy Economics, Elsevier, vol. 37(C), pages 40-51.
  2. Peter C.B. Phillips & Shu-Ping Shi & Jun Yu, 2012. "Specification Sensitivity in Right-Tailed Unit Root Testing for Explosive Behavior," Cowles Foundation Discussion Papers 1842, Cowles Foundation for Research in Economics, Yale University.
  3. Taipalus, Katja, 2012. "Detecting asset price bubbles with time-series methods," Scientific Monographs E:47/2012, Bank of Finland.
  4. Yiu, Matthew S. & Yu, Jun & Jin, Lu, 2013. "Detecting bubbles in Hong Kong residential property market," Journal of Asian Economics, Elsevier, vol. 28(C), pages 115-124.
  5. Anton Skrobotov, 2013. "Double Unit Roots Testing, GLS-detrending and Uncertainty over the Initial Conditions," Working Papers 0083, Gaidar Institute for Economic Policy, revised 2013.
  6. Vipin Arora & Pedro Gomis-Porqueras & Shuping Shi, 2011. "Testing for Explosive Behaviour in Relative Inflation Measures: Implications for Monetary Policy," Development Research Unit Working Paper Series 37-11, Monash University, Department of Economics.
  7. Etienne, Xiaoli L. & Irwin, Scott H. & Garcia, Philip, 2014. "Bubbles in food commodity markets: Four decades of evidence," Journal of International Money and Finance, Elsevier, vol. 42(C), pages 129-155.
  8. Taipalus , Katja, 2012. "Signaling asset price bubbles with time-series methods," Research Discussion Papers 7/2012, Bank of Finland.
  9. Yoon, Gawon, 2012. "Explosive U.S. budget deficit," Economic Modelling, Elsevier, vol. 29(4), pages 1076-1080.
  10. Bettendorf, Timo & Chen, Wenjuan, 2013. "Are there bubbles in the Sterling-dollar exchange rate? New evidence from sequential ADF tests," Economics Letters, Elsevier, vol. 120(2), pages 350-353.
  11. Gustavo Adolfo HERNANDEZ DIAZ & Gabriel PIRAQUIVE GALEANO, 2014. "Evolución de los precios de la vivienda en Colombia," ARCHIVOS DE ECONOMÍA 011208, DEPARTAMENTO NACIONAL DE PLANEACIÓN.
  12. Chen, Wenjuan & Bettendorf, Timo, 2013. "Are There Bubbles in the Sterling-dollar Exchange Rate? New Evidence from Sequential ADF Tests," Annual Conference 2013 (Duesseldorf): Competition Policy and Regulation in a Global Economic Order 80002, Verein für Socialpolitik / German Economic Association.

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