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

TL;DR

This paper challenges the use of Pearson correlations for financial networks by adopting local Gaussian correlation to construct tail-based networks (negative-tail and positive-tail) from SSE stock returns (2004–2019). It systematically analyzes network structure and resilience using MST/PMFG/TMFG filtering, focusing on centrality, path length, and entropy, and contrasts results with conventional Pearson networks. The findings show that negative-tail LGCNETs are more informative about market risk, exhibiting stronger propagation and lower resilience, particularly during domestic crashes, while Pearson networks underrepresent these dynamics. The work suggests reevaluating prior conclusions with the local Gaussian framework and highlights the broader applicability of tail-aware, nonlinear dependence measures in financial networks.

Abstract

Financial networks based on Pearson correlations have been intensively studied. However, previous studies may have led to misleading and catastrophic results because of several critical shortcomings of the Pearson correlation. The local Gaussian correlation coefficient, a new measurement of statistical dependence between variables, has unique advantages including capturing local nonlinear dependence and handling heavy-tailed distributions. This study constructs financial networks using the local Gaussian correlation coefficients between tail regions of stock returns in the Shanghai Stock Exchange. The work systematically analyzes fundamental network metrics including node centrality, average shortest path length, and entropy. Compared with the local Gaussian correlation network among positive tails and the conventional Pearson correlation network, the properties of the local Gaussian correlation network among negative tails are more sensitive to the stock market risks. This finding suggests researchers should prioritize the local Gaussian correlation network among negative tails. Future work should reevaluate existing findings using the local Gaussian correlation method.

Figures (6)

• Figure 1: SSCI performance over the period from April 7, 2004 to December 31, 2019. Based on SSCI fluctuations, the period is segmented into ten periods as colored regions indicate. Red and green regions represent bear and bull markets, respectively.
• Figure 2: Boxplots of correlation coefficients across ten periods. Green boxes, violet boxes, and gray boxes indicate local Gaussian correlation coefficients among negative tails, local Gaussian correlation coefficients among positive tails, and conventional Pearson correlation coefficients.
• Figure 3: Pairwise overlap of top-ten stocks in filtered correlation networks during the last period. The left and right panels depict strength and eigenvector centrality rankings, respectively. See main text for details.
• Figure 4: Tail shape parameters of network centrality distributions in ten periods. The first and second rows are for strength and eigenvector centralities, respectively. The first, second, and third columns are for MST, PMFG, and TMFG filtering methodologies, respectively. Red, green, and black data markers are for negative-tail LGCNETs, positive-tail LGCNETs, and Pearson correlation networks, respectively. Vertical error bars are 95% confidence intervals. These panels share common legends.
• Figure 5: Network's average shortest path length across ten periods. The left, middle, and right panels are for MST, PMFG, and TMFG filtering methodologies, respectively. Red, green, and black data markers are for negative-tail LGCNETs, positive-tail LGCNETs, and Pearson correlation networks, respectively. Violet vertical bands indicate the periods of the 2007-2008 global financial crisis and the 2015-2016 Chinese stock market turbulence. These panels share common legends.