Significance of Log-Periodic Precursors to Financial Crashes

38 Pages Posted: 25 Jul 2001  

Anders Johansen

Riso National Laboratory - Wind Energy Department; University of Copenhagen, Niels Bohr. Inst.; University of California, Los Angeles (UCLA) - Institute of Geophysics and Planetary Physics

Didier Sornette

Swiss Finance Institute; ETH Zürich - Department of Management, Technology, and Economics (D-MTEC)

Multiple version iconThere are 2 versions of this paper

Date Written: June 2001

Abstract

We clarify the status of log-periodicity associated with speculative bubbles preceding financial crashes. In particular, we address Feigenbaum's [2001] criticism and show how it can be rebuked. Feigenbaum's main result is as follows: "the hypothesis that the log-periodic component is present in the data cannot be rejected at the 95% confidence level when using all the data
prior to the 1987 crash; however, it can be rejected by removing the last year of data." (e.g., by removing 15% of the data closest to the critical point). We stress that it is naive to analyze a critical point phenomenon, i.e., a power law divergence, reliably by removing the most important part of the data closest to the critical point. We also present the history of log-periodicity in the present context explaining its essential features and why it may be important. We offer an extension of the rational expectation bubble model for general and arbitrary risk-aversion within the general stochastic discount factor theory. We suggest guidelines for using log-periodicity and explain how to develop and interpret statistical tests of log-periodicity. We discuss the issue of prediction based on our results and the evidence of outliers in the distribution of drawdowns. New statistical tests demonstrate that the 1% to 10% quantile of the largest events of the population of drawdowns of the Nasdaq composite index and of the Dow Jones Industrial Average index belong to a distribution significantly different from the rest of the population. This suggests that very large drawdowns result from an amplification mechanism that may make them more predictable than smaller market moves.

Suggested Citation

Johansen, Anders and Sornette, Didier, Significance of Log-Periodic Precursors to Financial Crashes (June 2001). Available at SSRN: https://ssrn.com/abstract=274968 or http://dx.doi.org/10.2139/ssrn.274968

Anders Johansen (Contact Author)

Riso National Laboratory - Wind Energy Department ( email )

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University of Copenhagen, Niels Bohr. Inst. ( email )

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University of California, Los Angeles (UCLA) - Institute of Geophysics and Planetary Physics ( email )

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Didier Sornette

Swiss Finance Institute ( email )

c/o University of Geneve
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Switzerland

ETH Zürich - Department of Management, Technology, and Economics (D-MTEC) ( email )

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