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

Vladimir Filimonov, Guilherme Demos and Didier Sornette
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Vladimir Filimonov: Swiss Federal Institute of Technology Zurich (ETH Zurich)
Didier Sornette: Swiss Finance Institute; ETH Zürich - Department of Management, Technology, and Economics (D-MTEC)

No 16-12, Swiss Finance Institute Research Paper Series from Swiss Finance Institute

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 (search for similar items in EconPapers)
JEL-codes: C13 C18 C53 G01 G17 (search for similar items in EconPapers)
Pages: 40 pages
Date: 2016-02
New Economics Papers: this item is included in nep-rmg
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Working Paper: Modified Profile Likelihood Inference and Interval Forecast of the Burst of Financial Bubbles (2016)
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Persistent link: https://EconPapers.repec.org/RePEc:chf:rpseri:rp1612

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