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Significance of log-periodic precursors to financial crashes | | D. Sornette
; A. Johansen
; | | Date: |
26 Jun 2001 | | Journal: | Quantitative Finance 1 (4), 452-471 (2001) | | Subject: | Statistical Mechanics | cond-mat.stat-mech | | Affiliation: | Univ. Nice/CNRS and UCLA) and A. Johansen (The Niels Bohr Institute | | 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. | | Source: | arXiv, cond-mat/0106520 | | Services: | Forum | Review | PDF | Favorites | |
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