Finding Core Balanced Modules in Statistically Validated Stock Networks

2025-08-06

AI Summary

Conventional threshold-based methods for constructing stock networks suffer from subjectivity, binary-only edge representation, and inability to capture negative correlations. Method: We propose a statistically significant signed network modeling framework. We formally define and theoretically prove the existence and size characteristics of the Largest Strongly Correlated Balanced Module (LSCBM) in random signed graphs. Leveraging the t-test on Pearson correlation coefficients, we construct a significance-aware correlation network and design the MaxBalanceCore heuristic algorithm to efficiently identify the LSCBM, exploiting network sparsity to ensure scalability to networks with tens of thousands of nodes. Contribution/Results: Empirical analysis on China’s A-share market reveals that the LSCBM expands during market stress periods and contracts during stable periods; its constituent stocks exhibit pronounced annual turnover. Critically, the LSCBM accurately captures the dynamic evolution of industry-dominant structures, establishing a novel paradigm for financial network analysis.

Technology Category

• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Machine Learning: Graph-based Machine Learning
• Natural Language Processing: Sentiment Analysis, Stylistic Analysis, and Argument Mining

Application Category

• Social Networks and Social Media: Social media analysis through the lenses of networks
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Traditional threshold-based stock networks suffer from subjective parameter selection and inherent limitations: they constrain relationships to binary representations, failing to capture both correlation strength and negative dependencies. To address this, we introduce statistically validated correlation networks that retain only statistically significant correlations via a rigorous t-test of Pearson coefficients. We then propose a novel structure termed the largest strong-correlation balanced module (LSCBM), defined as the maximum-size group of stocks with structural balance (i.e., positive edge-ign products for all triplets) and strong pairwise correlations. This balance condition ensures stable relationships, thus facilitating potential hedging opportunities through negative edges. Theoretically, within a random signed graph model, we establish LSCBM's asymptotic existence, size scaling, and multiplicity under various parameter regimes. To detect LSCBM efficiently, we develop MaxBalanceCore, a heuristic algorithm that leverages network sparsity. Simulations validate its efficiency, demonstrating scalability to networks of up to 10,000 nodes within tens of seconds. Empirical analysis demonstrates that LSCBM identifies core market subsystems that dynamically reorganize in response to economic shifts and crises. In the Chinese stock market (2013-2024), LSCBM's size surges during high-stress periods (e.g., the 2015 crash) and contracts during stable or fragmented regimes, while its composition rotates annually across dominant sectors (e.g., Industrials and Financials).

Problem

• Overcome subjective parameter selection in stock networks
• Identify stable stock groups with strong correlations
• Detect dynamic market subsystems during economic shifts

Innovation

• Statistically validated correlation networks via t-test
• Largest strong-correlation balanced module (LSCBM) definition
• MaxBalanceCore heuristic algorithm for efficiency