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

2016/02/26 by Vladimir Filimonov, Filimonov, Vladimir, Guilherme Demos +3 · 1 citation
Economics, Econometrics and Finance · #Complex Systems and Time Series Analysis #Market Dynamics and Volatility #Financial Risk and Volatility Modeling

paper · pdf · doi:10.48550/arxiv.1602.08258

Abstract

We present a detailed methodological study of the application of the modified\nprofile likelihood method for the calibration of nonlinear financial models\ncharacterised by a large number of parameters. We apply the general approach to\nthe Log-Periodic Power Law Singularity (LPPLS) model of financial bubbles. This\nmodel is particularly relevant because one of its parameters, the critical time\nt_c signalling the burst of the bubble, is arguably the target of choice for\ndynamical risk management. However, previous calibrations of the LPPLS model\nhave shown that the estimation of t_c is in general quite unstable. Here, we\nprovide a rigorous likelihood inference approach to determine t_c, which\ntakes into account the impact of the other nonlinear (so-called "nuisance")\nparameters for the correct adjustment of the uncertainty on t_c. This\nprovides a rigorous interval estimation for the critical time, rather than a\npoint estimation in previous approaches. As a bonus, the interval estimations\ncan also be obtained for the nuisance parameters (m,\ω, damping), which\ncan be used to improve filtering of the calibration results. We show that the\nuse of the modified profile likelihood method dramatically reduces the number\nof local extrema by constructing much simpler smoother log-likelihood\nlandscapes. The remaining distinct solutions can be interpreted as genuine\nscenarios that unfold as the time of the analysis flows, which can be compared\ndirectly via their likelihood ratio. Finally, we develop a multi-scale profile\nlikelihood analysis to visualize the structure of the financial data at\ndifferent scales (typically from 100 to 750 days). We test the methodology\nsuccessfully on synthetic price time series and on three well-known historical\nfinancial bubbles.\n

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