Nonlinearity in stock networks

TL;DR

This paper investigates the role of nonlinearity in stock networks, showing that much of the observed nonlinearity is due to univariate non-Gaussianity and nonstationarity, with implications for network analysis during financial crises.

Contribution

It introduces a systematic multi-step approach to quantify, correct, and analyze nonlinearity in stock networks, clarifying its sources and effects on network properties.

Findings

Most apparent nonlinearity stems from univariate non-Gaussianity.

Nonstationarity in specific stocks influences perceived nonlinearity.

Financial crises induce strong nonlinear dependencies among stocks.

Abstract

Stock networks, constructed from stock price time series, are a well-established tool for the characterization of complex behavior in stock markets. Following Mantegna's seminal paper, the linear Pearson's correlation coefficient between pairs of stocks has been the usual way to determine network edges. Recently, possible effects of nonlinearity on the graph-theoretical properties of such networks have been demonstrated when using nonlinear measures such as mutual information instead of linear correlation. In this paper, we quantitatively characterize the nonlinearity in stock time series and the effect it has on stock network properties. This is achieved by a systematic multi-step approach that allows us to quantify the nonlinearity of coupling; correct its effects wherever it is caused by simple univariate non-Gaussianity; potentially localize in space and time any remaining strong sources of this nonlinearity; and, finally, study the effect nonlinearity has on global network properties. By applying this multi-step approach to stocks included in three prominent indices (NYSE100, FTSE100 and SP500), we establish that the apparent nonlinearity that has been observed is largely due to univariate non-Gaussianity. Furthermore, strong nonstationarity in a few specific stocks may play a role. In particular, the sharp decrease in some stocks during the global financial crisis of 2008 gives rise to apparent nonlinear dependencies among stocks.