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DYNAMIC BIFURCATIONS ON FINANCIAL MARKETS
M. Kozłowska, M. Denys, M. Wiliński, G. Link, T. Gubiec, T.R. Werner, R. Kutner Faculty of Physics University of Warsaw
&
Z.R. Struzik
The University of Tokyo and RIKEN Brain Science Institute, Japan
Index WIG of the Warsaw Stock Exchange (GPW)
2004-02-06 – 2007-07-06 - 2009-05-18
DAX: 2003-09-04 – 2007-07-13 - 2009-07-01
Sale of new family houses in USA
1990-01 - 2009-03
(dissertation of K. Pawlikowska)
DJIA: 2005-03-16 – 2007-10-09 - 2009-06-09
Detrended signals: WIG, DAX, DJIA
WIG, DAX, DJIA:
variance (monthly average).
Definition of threshold by spike
WIG: cumulative variance. Bimodal situation
WIG, DAX, DJIA:
cumulative skewness
Application of catastrophe theory to financial markets.
Hypothesis: critical bifurcation transition
Application of catastrophe theory to financial markets.
Catastrophic bifurcation transition – the potential approach
Detrended successive signals for WIG.
Two time scales: (i) daily (fast) one and (ii) monthly (slow) one
Application of catastrophe theory to financial markets.
Critical slowing down
DAX: (Sub)critical bifurcation transition
Time [month]
Sale [thousand]
WIG: Reddened of power spectrum
The goal is to find this folded curve
on a financial market
The question of whether the early-warning signals are present in financial markets continues to fascinate both the research community and general public. Interestingly, such early-warning signals have recently been identified and explained to be a consequence of catastrophic bifurcation (CB) phenomenon observed in multiple physical systems*, e.g., in ecosystems (changes in states of coral reefs, colaps of vegetation in semi-arid ecosystem ), in geophysics ( earth quake, volcano eruption, abrupt shift in ocean circulation or in climate) and in medicine (epileptic seizure and asthma attack). In the present work we provide an analogical, positive identification of such phenomenon in the context of a well-defined daily bubble on a financial market typical of stock exchange of small and middle to large capitalisations. This we obtained by considering and verifying a list of indicators (following from CB) of a WIG (Warsaw Stock Exchange Index) bubble on the Warsaw Stock Exchange, induced by the recent worldwide financial crisis. Technically, we focus on the largest relatively narrow peak (of one quarter width) in the time-dependent variance of detrended index WIG. In comparison with other peaks, this peak looks like a spike. By using several indicators within the range of the spike , such as: (i) a sudden strong increase in the variance and bimodal structure of the accumulative variance, (ii) linear indicators, such us the lag-1 autocorrelation function and AR(1) coefficient, both approaching their maximal values, (iii) the corresponding behaviour of recovery rate and time, (iv) reddened power spectra, and (v) nonlinear indicators such as strongly nonvanishing accumulative skewnees, we verify that indeed considered local spike seems to be the result of some catastrophic bifurcation.
* M. Scheffer et al., Nature 491 (2009), 53-59
8 Polish Symposium on Econo- and Sociophysics, Rzeszów 2015
Conclusions
We suggest that:
The bifurcation catastrophic transition exists
on financial markets and perhaps constitutes
an alert signal before a global crash.
We defined the foundation of a new project:
Systematic comparison of bifurcation catastrophic transitions for all stock market crashes within the last 100 years.