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A Consistent Model of ‘Explosive’Financial Bubbles With Mean-Reversing Residuals

Li Lin, Ruo En Ren and Didier Sornette
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Li Lin: ETH Zurich and Beihang University
Ruo En Ren: Beihang University
Didier Sornette: ETH Zurich and Swiss Finance Institute

No 09-14, Swiss Finance Institute Research Paper Series from Swiss Finance Institute

Abstract: We present a self-consistent model for explosive financial bubbles, which combines a mean-reverting volatility process and a stochastic conditional return which reflects nonlinear positive feedbacks and continuous updates of the investors’ beliefs and sentiments. The conditional expected returns exhibit faster-than-exponential acceleration decorated by accelerating oscillations, called “log-periodic power law.” Tests on residuals show a remarkable low rate (0.2%) of false positives when applied to a GARCH benchmark. When tested on the S&P500 US index from Jan. 3, 1950 to Nov. 21, 2008, the model correctly identifies the bubbles ending in Oct. 1987, in Oct. 1997, in Aug. 1998 and the ITC bubble ending on the first quarter of 2000. Different unit-root tests confirm the high relevance of the model specification. Our model also provides a diagnostic for the duration of bubbles: applied to the period before Oct. 1987 crash, there is clear evidence that the bubble started at least 4 years earlier. We confirm the validity and universality of the volatility-confined LPPL model on seven other major bubbles that have occurred in the World in the last two decades. Using Bayesian inference, we find a very strong statistical preference for our model compared with a standard benchmark, in contradiction with Chang and Feigenbaum [2006] which used a unit-root model for residuals.

Keywords: Rational bubbles; mean reversal; positive feedbacks; finite-time singularity; superexponential growth; Bayesian analysis; log-periodic power law (search for similar items in EconPapers)
JEL-codes: G01 G17 C11 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm
Date: 2009-05
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