A stable and robust calibration scheme of the log-periodic power law model

V. Filimonov and D. Sornette

Physica A: Statistical Mechanics and its Applications, 2013, vol. 392, issue 17, 3698-3707

Abstract: We present a simple transformation of the formulation of the log-periodic power law formula of the Johansen–Ledoit–Sornette (JLS) 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 the most crucial nonlinear parameter, the critical time tc, defined in the JLS model 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 a 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 (search for similar items in EconPapers)
Date: 2013
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (72)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:392:y:2013:i:17:p:3698-3707

DOI: 10.1016/j.physa.2013.04.012

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