Modified Profile Likelihood Inference and Interval Forecast of the Burst of Financial Bubbles

40 Pages Posted: 1 Mar 2016

See all articles by Vladimir Filimonov

Vladimir Filimonov

Swiss Federal Institute of Technology Zurich (ETH Zurich)

Guilherme Demos

ETH Zurich

Didier Sornette

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

Date Written: February 26, 2016

Abstract

We present a detailed methodological study of the application of the modified profile likelihood method for the calibration of nonlinear financial models characterised by a large number of parameters. We apply the general approach to the Log-Periodic Power Law Singularity (LPPLS) model of financial bubbles. This model is particularly relevant because one of its parameters, the critical time tc signalling the burst of the bubble, is arguably the target of choice for dynamical risk management. However, previous calibrations of the LPPLS model have shown that the estimation of tc is in general quite unstable. Here, we provide a rigorous likelihood inference approach to determine tc, which takes into account the impact of the other nonlinear (so-called "nuisance") parameters for the correct adjustment of the uncertainty on tc. This provides a rigorous interval estimation for the critical time, rather than a point estimation in previous approaches. As a bonus, the interval estimations can also be obtained for the nuisance parameters (m,w, damping), which can be used to improve filtering of the calibration results. We show that the use of the modified profile likelihood method dramatically reduces the number of local extrema by constructing much simpler smoother log-likelihood landscapes. The remaining distinct solutions can be interpreted as genuine scenarios that unfold as the time of the analysis flows, which can be compared directly via their likelihood ratio. Finally, we develop a multi-scale profile likelihood analysis to visualize the structure of the financial data at different scales (typically from 100 to 750 days). We test the methodology successfully on synthetic price time series and on three well-known historical financial bubbles.

Keywords: financial bubbles; crashes; inference; nuisance parameters; modified profile likelihood; nonlinear regression; JLS model; log-periodic power law; finite time singularity: nonlinear optimization

JEL Classification: C13, C18, C53, G01, G17

Suggested Citation

Filimonov, Vladimir and Demos, Guilherme and Sornette, Didier, Modified Profile Likelihood Inference and Interval Forecast of the Burst of Financial Bubbles (February 26, 2016). Swiss Finance Institute Research Paper No. 16-12. Available at SSRN: https://ssrn.com/abstract=2739832 or http://dx.doi.org/10.2139/ssrn.2739832

Vladimir Filimonov

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

Scheuchzerstrasse 7, SEC F3
Zurich, CH-8092
Switzerland

Guilherme Demos

ETH Zurich ( email )

Rämistrasse 101
ZUE F7
Zürich, 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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