Relationship between Entropy and Dimension of Financial Correlation-Based Network

Area of Science:

• Quantitative Finance
• Network Science
• Complexity Theory

Background:

• Financial markets exhibit complex network structures.
• Characterizing this complexity is crucial for understanding market dynamics.
• Existing methods like the power law index have limitations.

Purpose of the Study:

• To develop and apply a novel dimension-based analysis for financial correlation networks.
• To characterize the complexity of financial networks.
• To compare the efficacy of this new method against traditional approaches.

Main Methods:

• Generalizing the volume-based dimension for correlation networks.
• Establishing the relationship between the Rényi index and the volume-based dimension.
• Analyzing dimension sequences against randomized time series benchmarks.
• Empirical analysis using real stock market data from three countries.

Main Results:

• The generalized volume-based dimension is well-defined for correlation networks.
• A clear relationship between the Rényi index and the volume-based dimension was established.
• The dimension sequence effectively characterizes network complexity and deviation from benchmarks.
• The proposed method demonstrated superior accuracy in capturing structural differences compared to the power law index in certain cases.

Conclusions:

• The dimension-based analysis provides a robust framework for quantifying financial network complexity.
• This novel approach offers enhanced insights into market structure compared to conventional methods.
• The findings have implications for financial risk management and market analysis.