Nonparametric Analyses of LogPeriodic Precursors to Financial Crashes
Abstract
We apply two nonparametric methods to further test the hypothesis that logperiodicity characterizes the detrended price trajectory of large financial indices prior to financial crashes or strong corrections. The term "parametric" refers here to the use of the logperiodic power law formula to fit the data; in contrast, "nonparametric" refers to the use of general tools such as Fourier transform, and in the present case the Hilbert transform and the socalled (H, q)analysis. The analysis using the (H, q)derivative is applied to seven time series ending with the October 1987 crash, the October 1997 correction and the April 2000 crash of the Dow Jones Industrial Average (DJIA), the Standard & Poor 500 and Nasdaq indices. The Hilbert transform is applied to two detrended price time series in terms of the ln(t_{c}t) variable, where t_{c} is the time of the crash. Taking all results together, we find strong evidence for a universal fundamental logfrequency f=1.02±0.05 corresponding to the scaling ratio λ=2.67±0.12. These values are in very good agreement with those obtained in earlier works with different parametric techniques. This note is extracted from a long unpublished report with 58 figures available at , which extensively describes the evidence we have accumulated on these seven time series, in particular by presenting all relevant details so that the reader can judge for himself or herself the validity and robustness of the results.
 Publication:

International Journal of Modern Physics C
 Pub Date:
 2003
 DOI:
 10.1142/S0129183103005212
 arXiv:
 arXiv:condmat/0205531
 Bibcode:
 2003IJMPC..14.1107Z
 Keywords:

 Financial crashes;
 critical phenomena;
 discrete scale invariance;
 logperiodicity;
 Hilbert transform;
 generalized qanalysis;
 Condensed Matter  Statistical Mechanics;
 Quantitative Finance  Statistical Finance
 EPrint:
 Latex document 13 pages + 58 eps figures