The local Gaussian correlation networks among return tails in the Chinese stock market

Abstract The financial networks based on Pearson's correlation are intensively studied. However, the previous studies may lead to misleading and catastrophic results because of several critical shortcomings of Pearson's correlation. The Local Gaussian correlation coefficient, a new measurement of statistical dependence between variables, has some new features that can capture the nonlinear correlation and are suitable for heavy-tailed variables. This paper constructs local Gaussian correlation networks using the local Gaussian correlation coefficients among both negative tails and positive tails of returns of stocks traded in the Shanghai Stock Exchange. Compared with the local Gaussian correlation network among positive tails and the network based on Pearson's correlation, the results show that the local Gaussian correlation network among negative tails better reflects the stock market risks. This finding suggests that we must pay more attention to the local Gaussian correlation network among negative tails rather than Pearson's network. In the future, it is worth reexamining the related studies using the local Gaussian correlation.