# A Bayesian analysis of log-periodic precursors to financial crashes

*George Chang* and
*James Feigenbaum* ()

*Quantitative Finance*, 2006, vol. 6, issue 1, 15-36

**Abstract:**
A large number of papers have been written by physicists documenting an alleged signature of imminent financial crashes involving so-called log-periodic oscillations-oscillations which are periodic with respect to the logarithm of the time to the crash. In addition to the obvious practical implications of such a signature, log-periodicity has been taken as evidence that financial markets can be modelled as complex statistical-mechanics systems. However, while many log-periodic precursors have been identified, the statistical significance of these precursors and their predictive power remain controversial in part because log-periodicity is ill-suited for study with classical methods. This paper is the first effort to apply Bayesian methods in the testing of log-periodicity. Specifically, we focus on the Johansen-Ledoit-Sornette (JLS) model of log periodicity. Using data from the S&P 500 prior to the October 1987 stock market crash, we find that, if we do not consider crash probabilities, a null hypothesis model without log-periodicity outperforms the JLS model in terms of marginal likelihood. If we do account for crash probabilities, which has not been done in the previous literature, the JLS model outperforms the null hypothesis, but only if we ignore the information obtained by standard classical methods. If the JLS model is true, then parameter estimates obtained by curve fitting have small posterior probability. Furthermore, the data set contains negligible information about the oscillation parameters, such as the frequency parameter that has received the most attention in the previous literature.

**Keywords:** Financial crashes; Bayesian inference; Log-periodicity (search for similar items in EconPapers)

**Date:** 2006

**References:** View references in EconPapers View complete reference list from CitEc

**Citations:** View citations in EconPapers (21) Track citations by RSS feed

**Downloads:** (external link)

http://www.tandfonline.com/doi/abs/10.1080/14697680500511017 (text/html)

Access to full text is restricted to subscribers.

**Related works:**

This item may be available elsewhere in EconPapers: Search for items with the same title.

**Export reference:** BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text

**Persistent link:** https://EconPapers.repec.org/RePEc:taf:quantf:v:6:y:2006:i:1:p:15-36

**Ordering information:** This journal article can be ordered from

http://www.tandfonline.com/pricing/journal/RQUF20

**DOI:** 10.1080/14697680500511017

Access Statistics for this article

Quantitative Finance is currently edited by *Michael Dempster* and *Jim Gatheral*

More articles in Quantitative Finance from Taylor & Francis Journals

Bibliographic data for series maintained by Chris Longhurst ().