Stock networks constitute a well established tool for characterization of complex behavior in stock markets. The networks are constructed from time series of stock prices. Since Mantegnaseminal paper the linear Pearson's correlation coefficient between pairs of stocks is used to determine network edges. Recently, possible effects of nonlinearity on graph characteristics 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. It is achieved by a systematic multi-step approach , that allows 1. to quantify the nonlinearity of coupling , 2. to correct its effects wherever it is caused by simple univariate non-Gaussianity , 3. to potentially localize in space and time any remaining strong sources of this nonlinearity , andfinally, 4. to study the effect the nonlinearity has on global network properties. By applying the presented approach to stocks included in three prominent indices (NYSE100, FTSE100 and SP500), we document that most of the apparent nonlinearity is due to univariate non-Gaussianity. Further , strong nonstationarity in a few specific stocks may play a role. In particular, the sharp decrease of some stocks during the global finance crisis in 2008 gives rise to apparent nonlinear dependences among stocks.
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.
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