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Testing for Multiple Bubbles: Limit Theory of Real Time Detectors

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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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File URL: http://cowles.yale.edu/sites/default/files/files/pub/d19/d1915.pdf
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Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1915.

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Length: 75 pages
Date of creation: Sep 2013
Publication status: Published in International Economic Review (November 2015), 56(4): 1079-1134
Handle: RePEc:cwl:cwldpp:1915
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Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Web page: http://cowles.yale.edu/

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Order Information: Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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  1. 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.
  2. 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, 02.
  3. 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.
  4. 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.
  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. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
  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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