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

Paper: arXiv 2510.21165

Authors: Peng Liu

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.

Complexity vs Empirical Score

• Math Complexity: 5.5/10
• Empirical Rigor: 6.5/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper introduces a solid methodology by replacing traditional Pearson correlation with local Gaussian correlations to capture non-linear tail dependencies in complex financial networks. The empirical analysis covers a large dataset from the Shanghai Stock Exchange across distinct market regimes (2004–2019), showing clear practical insights into tail-risk sensitivity.

Research Flowchart

  flowchart TD
    A[Goal: Analyze financial tail dependencies in SSE using Local Gaussian Correlation] --> B[Data Input: Shanghai Stock Exchange SSE stock return series]
    B --> C[Compute Local Gaussian Correlation Coefficients in Tail Regions]
    C --> D[Construct Financial Networks: Positive Tails, Negative Tails & Pearson]
    D --> E[Analyze Network Metrics: Centrality, Path Length & Entropy]
    E --> F[Findings: Negative Tail LGC Networks are most sensitive to market risks]
    F --> G[Outcome: Prioritize Negative Tail LGC over Pearson for risk analysis]

Cited References (41)

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2. The multilayer nature of ecological networks (2017) — link
3. Tail event driven networks of SIFIs (2019) — link
4. Time persistence of climate and carbon flux networks (2024) — link
5. Identifying the optimal node group of carbon emission efficiency correlation network in China based on pinning control theory (2024) — link
6. Optimal resilience of modular interacting networks (2021) — link
7. The physics of financial networks (2021) — link
8. Anti-correlation network among China A-shares — → 2404.00028

1 of 41 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.