Nonlinearity in stock networks

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.