Significance of logperiodic precursors to financial crashes
Abstract
We clarify the status of logperiodicity 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 logperiodic 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 logperiodicity 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 riskaversion within the general stochastic discount factor theory. We suggest guidelines for using logperiodicity and explain how to develop and interpret statistical tests of logperiodicity. 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.
 Publication:

arXiv eprints
 Pub Date:
 June 2001
 arXiv:
 arXiv:condmat/0106520
 Bibcode:
 2001cond.mat..6520S
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Quantitative Finance  Statistical Finance
 EPrint:
 Latex document of 38 pages including 16 eps figures and 3 tables, in press in Quantitative Finance