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Nonlinearity in stock networks.

David Hartman1, Jaroslav Hlinka1

  • 1Institute of Computer Science, Czech Academy of Sciences, Prague 182 07, Czech Republic.

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Summary
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Apparent nonlinearity in stock market networks is often due to non-Gaussian stock price distributions, not true nonlinear relationships. This study quantifies nonlinearity, corrects for non-Gaussianity, and reveals market dynamics, especially during the 2008 financial crisis.

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Area of Science:

  • Quantitative Finance
  • Network Science
  • Financial Econometrics

Background:

  • Stock networks analyze market complexity using stock price time series.
  • Traditionally, Pearson's correlation defines network edges, but nonlinear measures reveal different properties.

Purpose of the Study:

  • To quantitatively characterize nonlinearity in stock time series.
  • To assess the impact of nonlinearity on stock network properties.
  • To differentiate true nonlinearity from non-Gaussian effects.

Main Methods:

  • A systematic multi-step approach to quantify coupling nonlinearity.
  • Correction for nonlinearity caused by univariate non-Gaussianity.
  • Analysis of stock data from NYSE 100, FTSE 100, and S&P 500 indices.

Main Results:

  • Apparent nonlinearity in stock networks is primarily attributed to univariate non-Gaussianity.
  • Strong nonstationarity in specific stocks, particularly during the 2008 financial crisis, contributes to perceived nonlinear dependencies.
  • The study successfully localized sources of nonlinearity and assessed their impact on network properties.

Conclusions:

  • The influence of nonlinear measures on stock network analysis is largely explained by non-Gaussian distributions.
  • Market events like the 2008 crisis can induce temporary nonlinear dependencies.
  • A refined understanding of stock market dynamics requires accounting for non-Gaussianity and nonstationarity.