Non-linear correlation analysis in financial markets using hierarchical clustering

Paper: arXiv 2301.05080

Authors: J. E. Salgado-Hernández, Manan Vyas

Abstract

Distance correlation coefficient (DCC) can be used to identify new associations and correlations between multiple variables. The distance correlation coefficient applies to variables of any dimension, can be used to determine smaller sets of variables that provide equivalent information, is zero only when variables are independent, and is capable of detecting nonlinear associations that are undetectable by the classical Pearson correlation coefficient (PCC). Hence, DCC provides more information than the PCC. We analyze numerous pairs of stocks in S&P500 database with the distance correlation coefficient and provide an overview of stochastic evolution of financial market states based on these correlation measures obtained using agglomerative clustering.

Complexity vs Empirical Score

• Math Complexity: 0.0/10
• Empirical Rigor: 0.0/10
• Quadrant: Philosophers — conceptual discussion, limited math and data

Why this score: Scoring failed: Could not find valid JSON in LLM response: line 1 column 1 (char 0)

Research Flowchart

  flowchart TD
    A[Research Goal: Detect Non-linear Stock Correlations & Market Evolution] --> B[Data Input: S&P 500 Stock Price Time Series]
    B --> C[Compute Distance Correlation Coefficient - DCC]
    C --> D[Compare DCC with Pearson Correlation Coefficient - PCC]
    D --> E[Apply Agglomerative Hierarchical Clustering]
    E --> F[Key Outcomes: Uncover Non-linear Associations & Stochastic Market States]