Institutional Knowledge at Singapore Management University
Research Collection School Of Economics
School of Economics
8-2013
Testing for Multiple Bubbles 1: Historical Episodes of Exuberance and Collapse in the S&P 500
Peter C. B. Phillips
Singapore Management University, peterphillips@smu.edu.sg
Shu-Ping SHI
Jun Yu
Singapore Management University, yujun@smu.edu.sg
Follow this and additional works at: http://ink.library.smu.edu.sg/soe_research
Part of the Economics Commons
Citation
Phillips, Peter C. B.; SHI, Shu-Ping; and Yu, Jun. Testing for Multiple Bubbles 1: Historical Episodes of Exuberance and Collapse in the S&P 500. (2013). Research Collection School Of Economics.
Available at: http://ink.library.smu.edu.sg/soe_research/1510
This Working Paper is brought to you for free and open access by the School of Economics at Institutional Knowledge at Singapore Management
University. It has been accepted for inclusion in Research Collection School Of Economics by an authorized administrator of Institutional Knowledge at Singapore Management University. For more information, please email libIR@smu.edu.sg.
Testing for Multiple Bubbles 1: Historical Episodes of
Exuberance and Collapse in the S&P 500
Peter C. B. Phillips, Shu-Ping Shi and Jun Yu
August 2013
Paper No. 04 – 2013
ANY OPINIONS EXPRESSED ARE THOSE OF THE AUTHOR(S) AND NOT NECESSARILY THOSE OF
THE SCHOOL OF ECONOMICS, SMU
Testing for Multiple Bubbles 1: Historical Episodes of
Exuberance and Collapse in the S&P 500
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
July 28, 2013
Abstract
Recent work on econometric detection mechanisms has shown the e¤ectiveness of recursive procedures in identifying and dating …nancial bubbles. These procedures are useful
References: Ahamed, L., 2009, Lords of Finance: The Bankers Who Broke the World, Penguin Press, New York. Bhargava, A. 1986, On the theory of testing for unit roots in observed time series, Review of Economic Studies, 53, 369– Busetti, F., and A. M. R. Taylor, 2004, Tests of stationarity against a change in persistence, Journal of Econometrics, 123, 33– Campbell, J.Y., and Perron, P., 1991, Pitfalls and opportunities: what macroeconomists should know about unit roots Campbell, J.Y., and Shiller R.J., 1989, The dividend-price ratio and expectations of future dividends and discount factors Charemza, W.W., and Deadman, D.F., 1995, Speculative bubbles with stochastic explosive roots: the failure of unit root testing Chu, C.J., Stinchcombe, M., and White, H., 1996, Monitoring structural change. Econometrica, 64:1045-1065. Cochrane, J. H., 1992. Explaining the Variance of Price-Dividend Ratios. The Review of Financial Studies, 5(2), 243-280. Cochrane, J. H., 2005. Asset Pricing, Princeton: Princeton University Press. Cooper, G., 2008, The Origin of Financial Crises: Central Banks, Credit Bubbles and the E¢ cient Market Fallacy, Vintage Books, New York. 41 Diba, B.T., and Grossman, H.I., 1988, Explosive rational bubbles in stock prices? The American Economic Review, 78, 520– Evans, G.W., 1991, Pitfalls in testing for explosive bubbles in asset prices. The American Economic Review, 81, 922– Ferguson, N., 2008, The Ascent of Money, Penguin Press, New York. Funke, M., Hall, S., and Sola, M., 1994, Rational bubbles during Poland’ hyperin‡ s Gurkaynak, R. S., 2008, Econometric tests of asset price bubbles: taking stock. Journal of Economic Surveys, 22, 166– Hall, S.G., Psaradakis, Z., and Sola M., 1999, Detecting periodically collapsing bubbles: A markov-switching unit root test Homm, U., and Breitung, J., 2012. Testing for speculative bubbles in stock markets: a comparison of alternative methods. Journal of Financial Econometrics, 10(1), 198-231. Kim, J. Y. 2000, Detection of change in persistence of a linear time series, Journal of Econometrics, 95, 97– 116. Kindleberger, C. P., and Aliber, R. Z., 2005, Manias, Panics and Crashes; A History of Financial Crises, Hoboken, New Jersey: John Wiley and Sons, Inc. Lee, J. and P. C. B. Phillips, 2011, Asset Pricing with Financial Bubble Risk. Yale University, Working Paper. Pástor, Luboš and Pietro Veronesi, 2006, Was there a Nasdaq bubble in the late 1990s? Journal , Phillips, P.C.B., 1987, Time series regression with a unit root. Econometrica 55, 277-301. Phillips, P.C.B., and Perron, P., 1988, Testing for a unit root in time series regression. Biometrika, 75, 335– 346. 42 Phillips, P.C.B., and Magdalinos, T., 2007, Limit theory for moderate deviations from a unit Phillips, P. C. B. and V. Solo, 1992, Asymptotics for Linear Processes. Annals of Statistics 20, 971– Phillips, P.C.B., Shi, S., and Yu, J., 2013a, Speci…cation Sensitivity in Right-Tailed Unit Root Testing for Explosive Behavior Phillips, P.C.B., Shi, S., and Yu, J., 2013b. Testing for Multiple Bubbles 2: Limit Theory of Dating Algorithms Phillips, P.C.B., Wu, Y., and Yu, J., 2011, Explosive behavior in the 1990s Nasdaq: When did exuberance escalate asset values? International Economic Review, 52, 201-226. Phillips, P.C.B., and Yu, J., 2009, Limit theory for dating the origination and collapse of mildly explosive periods in time series data Phillips, P.C.B., and Yu, J., 2011, Dating the Timeline of Financial Bubbles During the Subprime Crisis, Quantitative Economics, 2, 455-491. Psaradakis, Z., Sola, M., and Spagnolo, F., 2001, A simple procedure for detecting periodically collapsing rational bubbles Shi, S., 2012. Speci…cation sensitivities in the Markov-switching unit root test for bubbles. van Norden, S. and Vigfusson, R., 1998, Avoiding the pitfalls: can regime-switching tests reliably detect bubbles? Studies in Nonlinear Dynamics & Econometrics, 3,1– West, K.D., 1988, Dividend Innovations and Stock Price Volatility. Econometrica, 56:37– 61. Before proving Theorem 1 we give conditions on the innovations and state two preliminary lemmas whose proofs follow directly by standard methods (Phillips, 1987; Phillips and Perron, 1988; Phillips and Solo, 1992).