[Paper Review] Anomaly Detection in Global Financial Markets with Graph Neural Networks and Nonextensive Entropy

Kleyton da Costa|arXiv (Cornell University)|Aug 5, 2023

Complex Systems and Time Series AnalysisEconomics, Econometrics and Finance3 citations

TL;DR

This paper proposes a graph neural network (GNN)-based anomaly detection framework for global financial markets using nonextensive Tsallis entropy to quantify uncertainty. By modeling stock correlations as a dynamic graph and training a Graph Autoencoder, the method detects anomalies that vary significantly across crisis, pre-crisis, and post-crisis periods, with the highest anomaly counts during crises and strong statistical differences in detection rates across periods.

ABSTRACT

Anomaly detection is a challenging task, particularly in systems with many variables. Anomalies are outliers that statistically differ from the analyzed data and can arise from rare events, malfunctions, or system misuse. This study investigated the ability to detect anomalies in global financial markets through Graph Neural Networks (GNN) considering an uncertainty scenario measured by a nonextensive entropy. The main findings show that the complex structure of highly correlated assets decreases in a crisis, and the number of anomalies is statistically different for nonextensive entropy parameters considering before, during, and after crisis.

Motivation & Objective

• To investigate the effectiveness of Graph Neural Networks (GNNs) in detecting anomalies within global financial market networks.
• To assess how nonextensive Tsallis entropy, parameterized by q, measures uncertainty and influences anomaly detection across different market regimes.
• To analyze structural changes in the global financial network before, during, and after a crisis, particularly in connectivity and centrality.
• To determine whether anomaly detection performance differs significantly across crisis phases using statistical hypothesis testing.

Proposed method

• Constructed a global financial market graph using correlation coefficients between stocks from major exchanges, with edges representing significant correlations (top 1% of absolute values).
• Represented the network as an adjacency matrix and applied a Graph Autoencoder (GAE) to learn a low-dimensional latent representation and reconstruct the original graph.
• Used Tsallis entropy (nonextensive entropy) with varying q-values as an anomaly score to quantify uncertainty in market dynamics.
• Trained the GAE on three distinct time periods: pre-crisis, during-crisis, and post-crisis, to evaluate model performance and reconstruction error.
• Applied t-tests to compare the mean number of detected anomalies across periods, testing for statistical significance.
• Analyzed network properties such as degree distribution, clustering coefficient, and edge density to characterize structural shifts during crises.

Experimental results

Research questions

• RQ1 How does the performance of GNN-based anomaly detection vary across different phases of financial market crises?
• RQ2 To what extent does the nonextensive entropy parameter q influence anomaly detection in pre-, during-, and post-crisis market conditions?
• RQ3 How do network structural properties such as edge density, clustering, and node centrality change during financial crises?
• RQ4 Are the numbers of detected anomalies statistically different between pre-crisis, crisis, and post-crisis periods?

Key findings

• The number of detected anomalies was highest during the crisis period, with a statistically significant difference compared to both pre- and post-crisis phases (p < 0.0001 for both comparisons).
• The GNN model showed higher reconstruction error in the pre- and post-crisis periods compared to during the crisis, indicating greater difficulty in learning network patterns outside crisis periods.
• During the crisis, the number of anomalies remained stable across different q-values, suggesting that the anomaly detection process is robust to entropy parameter variation in high-stress market conditions.
• The network became more sparse during the crisis, with a 33% decrease in edge count (from 455 to 294) and a 20 percentage point increase in nodes with no edges (from 39.52% to 59.97%).
• The mean degree increased significantly during the crisis (from 6.14 to 18.38), indicating higher connectivity among remaining nodes, while the maximum degree surged to 168, showing the emergence of highly connected assets.
• The clustering coefficient increased from 0.30 (pre-crisis) to 0.37 (post-crisis), suggesting a shift toward more clustered, localized network structures after the crisis.