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Application of the moving Lyapunov exponent to the S&P 500 index to predict major declines

Stefanos Tsakonas, Michael Hanias, Lykourgos Magafas and Loukas Zachilas

  • The S&P500 time-series can be modelled using non-linear models and Chaos theory.
  • The Moving Lyapunov Exponent can give early warnings preceding major drops of the S&P500 index.
  • The Moving Lyapunov Exponent can be used as a dynamic indicator of stability.

Predicting major downturns in financial markets is a popular topic among researchers. Improving the models used for this could benefit individuals, investment banks and financial institutions. The latest developments in econophysics provide additional forecasting tools that may aid this endeavor. This paper introduces an innovative method to identify early warnings for major declines in the Standard & Poor’s 500 (S&P 500) index. This method performs a nonlinear analysis of the logarithmic returns of the index and then uses the moving Lyapunov exponent as a dynamic indicator of stability. The results show that the fluctuating behavior of the moving Lyapunov exponent forms spikes, which may act as warning signals since they precede all significant events that have caused major drops in the S&P 500 index over the past 20 years, including the dot-com bubble, the Great Recession and the Covid-19 pandemic.

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