Empirical symptoms of catastrophic bifurcation transitions on financial markets: A phenomenological approach Marzena Kozłowska, Tomasz Gubiec, Ryszard.

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Presentation transcript:

Empirical symptoms of catastrophic bifurcation transitions on financial markets: A phenomenological approach Marzena Kozłowska, Tomasz Gubiec, Ryszard Kutner, Tomasz Werner Faculty of Physics, University of Warsaw and Zbigniew Struzik University of Tokyo & RIKEN Brain Science Institute, Japan VII Sympozjum Fizyki w Ekonomii I Naukach Społecznych UMCS Lublin, May 2014

Abrupt climate change

Catastrophic (critical) bifurcation transition in a real life. M. Scheffer et al., Nature 491 (2009), In medicine: epileptic seizure and asthma attack. In geophysics: earth quake, volcano eruption, abrupt shift in ocean circulation or in climate. In ecosystem degradation: changes in states of coral reefs, colaps of vegetation in semi-arid ecosystem. In physics: first order phase transitrions.

Index WIG of the Warsaw Stock Exchange (GPW) – Here, we consider the lhs bubble

DAX: – Here, we consider the lhs bubble

Beginning of new single-family house-buildings in US

Detrended signal and stochastic dynamics

The n oise of signal WIG

Sale of new single-family houses in US

WIG: variance (monthly sample average). Definition of threshold by spike

WIG: accumulative variance. Bimodal situation

Detrended successive signals for WIG. Two time scales: (i) daily t (fast) one and (ii) monthly (slow) one. Too large data dispersion for nonlinear analysis

Application of catastrophe theory to financial markets. Hypothesis: catastrophic bifurcation transition Complete approach requires nonlinear analysis

Application of catastrophe theory to financial markets. Catastrophic (critical) slowing down

Catastrophic bifurcation transition: force f and potential U

Plot of recovery rate

WIG: (Sub)catastrophic bifurcation transition ALERT: invstors should leave such a stock market

DAX: (Sub)catastrophic bifurcation transition ALERT: invstors should leave such a stock market

General conclusion: schematic scenario of stock market evolution generated by bifurcation transitions