Paper: arXiv 2312.16185

Abstract

Identifying and quantifying co-dependence between financial instruments is a key challenge for researchers and practitioners in the financial industry. Linear measures such as the Pearson correlation are still widely used today, although their limited explanatory power is well known. In this paper we present a much more general framework for assessing co-dependencies by identifying and interpreting linear and nonlinear causalities in the complex system of financial markets. To do so, we use two different causal inference methods, transfer entropy and convergent cross-mapping, and employ Fourier transform surrogates to separate their linear and nonlinear contributions. We find that stock indices in Germany and the U.S. exhibit a significant degree of nonlinear causality and that correlation, while a very good proxy for linear causality, disregards nonlinear effects and hence underestimates causality itself. The presented framework enables the measurement of nonlinear causality, the correlation-causality fallacy, and motivates how causality can be used for inferring market signals, pair trading, and risk management of portfolios. Our results suggest that linear and nonlinear causality can be used as early warning indicators of abnormal market behavior, allowing for better trading strategies and risk management.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 6.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs advanced nonlinear causality metrics (transfer entropy, convergent cross-mapping) and statistical physics tools like Fourier surrogates, indicating high mathematical density. It also applies these methods to extensive historical financial data (DAX and Dow-Jones) with rolling-window backtests, demonstrating significant empirical implementation.

Research Flowchart

  flowchart TD
  A["Research Goal:<br>Assess linear & nonlinear causality in financial markets"] --> B["Data Input:<br>Stock Indices (Germany & U.S.)"];
  B --> C{"Methodology Setup"};
  C --> D["Transfer Entropy<br>Convergent Cross-Mapping"];
  C --> E["Fourier Transform Surrogates<br>Isolate Linear vs. Nonlinear"];
  D --> F["Computational Process:<br>Quantify Causality & Correlation"];
  E --> F;
  F --> G{"Key Findings/Outcomes"};
  G --> H["Nonlinear Causality Exists<br>Linear correlation underestimates total causality"];
  G --> I["Applications:<br>Early warning, Pair trading, Risk management"];