A Stable and Robust Calibration Scheme of the Log-Periodic Power Law Model

RC Working Paper No. 11-002

20 Pages Posted: 19 Dec 2012

See all articles by Vladimir Filimonov

Vladimir Filimonov

Swiss Federal Institute of Technology Zurich (ETH Zurich)

Didier Sornette

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

Date Written: July 8, 2011

Abstract

We present a simple transformation of the formulation of the log-periodic power law formula of the Johansen-Ledoit-Sornette model of financial bubbles that reduces it to a function of only three nonlinear parameters. The transformation significantly decreases the complexity of the fitting procedure and improves its stability tremendously because the modified cost function is now characterized by good smooth properties with in general a single minimum in the case where the model is appropriate to the empirical data. We complement the approach with an additional subordination procedure that slaves two of the nonlinear parameters to what can be considered to be the most crucial nonlinear parameter, the critical time tc defined as the end of the bubble and the most probable time for a crash to occur. This further decreases the complexity of the search and provides an intuitive representation of the results of the calibration. With our proposed methodology, metaheuristic searches are not longer necessary and one can resort solely to rigorous controlled local search algorithms, leading to dramatic increase in efficiency. Empirical tests on the Shanghai Composite index (SSE) from January 2007 to March 2008 illustrate our findings.

Keywords: JLS model, financial bubbles, crashes, log-periodic power law, fit method, optimization

JEL Classification: G01, G17, C53

Suggested Citation

Filimonov, Vladimir and Sornette, Didier, A Stable and Robust Calibration Scheme of the Log-Periodic Power Law Model (July 8, 2011). RC Working Paper No. 11-002. Available at SSRN: https://ssrn.com/abstract=2190784 or http://dx.doi.org/10.2139/ssrn.2190784

Vladimir Filimonov

Swiss Federal Institute of Technology Zurich (ETH Zurich) ( email )

Scheuchzerstrasse 7, SEC F3
Zurich, CH-8092
Switzerland

Didier Sornette (Contact Author)

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

Scheuchzerstrasse 7
Zurich, ZURICH CH-8092
Switzerland
41446328917 (Phone)
41446321914 (Fax)

HOME PAGE: http://www.er.ethz.ch/

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

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