Predicting Financial Market Crashes Using Ghost Singularities
Smug, D; Ashwin, P; Sornette, D
Date: 29 March 2018
Journal
PLoS ONE
Publisher
Public Library of Science
Publisher DOI
Abstract
We analyse the behaviour of a non-linear model of coupled stock and bond prices exhibiting
periodically collapsing bubbles. By using the formalism of dynamical system theory, we explain what drives
the bubbles and how foreshocks or aftershocks are generated. A dynamical phase space representation of
that system coupled with standard ...
We analyse the behaviour of a non-linear model of coupled stock and bond prices exhibiting
periodically collapsing bubbles. By using the formalism of dynamical system theory, we explain what drives
the bubbles and how foreshocks or aftershocks are generated. A dynamical phase space representation of
that system coupled with standard multiplicative noise rationalises the log-periodic power law singularity
pattern documented in many historical financial bubbles. The notion of ‘ghosts of finite-time singularities’
is introduced and used to estimate the end of an evolving bubble, using finite-time singularities of an
approximate normal form near the bifurcation point. We test the forecasting skill of this method on
different stochastic price realisations and compare with Monte Carlo simulations of the full system.
Remarkably, the approximate normal form is significantly more precise and less biased. Moreover, the
method of ghosts of singularities is less sensitive to the noise realisation, thus providing more robust
forecasts.
Mathematics and Statistics
Faculty of Environment, Science and Economy
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