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Testing for Multiple Bubbles: Limit Theory of Real Time Detectors

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Abstract

This paper provides the limit theory of real time dating algorithms for bubble detection that were suggested in Phillips, Wu and Yu (2011, PWY) and Phillips, Shi and Yu (2013b, PSY). Bubbles are modeled using mildly explosive bubble episodes that are embedded within longer periods where the data evolves as a stochastic trend, thereby capturing normal market behavior as well as exuberance and collapse. Both the PWY and PSY estimates rely on recursive right tailed unit root tests (each with a different recursive algorithm) that may be used in real time to locate the origination and collapse dates of bubbles. Under certain explicit conditions, the moving window detector of PSY is shown to be a consistent dating algorithm even in the presence of multiple bubbles. The other algorithms are consistent detectors for bubbles early in the sample and, under stronger conditions, for subsequent bubbles in some cases. These asymptotic results and accompanying simulations guide the practical implementation of the procedures. They indicate that the PSY moving window detector is more reliable than the PWY strategy, sequential application of the PWY procedure and the CUSUM procedure.

Suggested Citation

  • Peter C.B. Phillips & Shu-Ping Shi & Jun Yu, 2013. "Testing for Multiple Bubbles: Limit Theory of Real Time Detectors," Cowles Foundation Discussion Papers 1915, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1915
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    File URL: http://cowles.yale.edu/sites/default/files/files/pub/d19/d1915.pdf
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    1. Peter C. B. Phillips & Yangru Wu & Jun Yu, 2011. "EXPLOSIVE BEHAVIOR IN THE 1990s NASDAQ: WHEN DID EXUBERANCE ESCALATE ASSET VALUES?," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 52(1), pages 201-226, February.
    2. Sonali Das & Rangan Gupta & Patrick T Kanda, 2010. "Bubbles in South African House Prices and their Impact on Consumption," Working Papers 201017, University of Pretoria, Department of Economics.
    3. Peter C. B. Phillips & Jun Yu, 2011. "Dating the timeline of financial bubbles during the subprime crisis," Quantitative Economics, Econometric Society, vol. 2(3), pages 455-491, November.
    4. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    5. 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.
    6. 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.
    7. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    8. 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.
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    Keywords

    Bubble duration; Consistency; Dating algorithm; Limit theory; Multiple bubbles; Real time detector;

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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