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Testing for Multiple Bubbles 2: Limit Theory of Real Time Detectors

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  • Peter C. B. Phillips

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

  • Shu-Ping Shi

    ()
    (The Australian National University)

  • Jun Yu

    ()
    (Singapore Management University)

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.

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Bibliographic Info

Paper provided by Singapore Management University, School of Economics in its series Working Papers with number 05-2013.

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Date of creation: Aug 2013
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Publication status: Published in SMU Economics and Statistics Working Paper Series
Handle: RePEc:siu:wpaper:05-2013

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

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  1. Peter C. B. Phillips & Jun Yu, 2009. "Dating the Timeline of Financial Bubbles During the Subprime Crisis," Finance Working Papers 23051, East Asian Bureau of Economic Research.
  2. Peter C.B.Phillips & Yangru Wu & Jun Yu, 2009. "Explosive Behavior in the 1990s Nasdaq: When Did Exuberance Escalate Asset Values?," Working Papers CoFie-03-2008, Sim Kee Boon Institute for Financial Economics.
  3. 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.
  4. 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.
  5. Peter C.B. Phillips, 1985. "Time Series Regression with a Unit Root," Cowles Foundation Discussion Papers 740R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1986.
  6. 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.
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