Measuring Linear and Nonlinear Causality Between Financial Markets

Summary

This paper presents a framework for studying dependence between financial instruments beyond conventional correlation. It applies transfer entropy and convergent cross-mapping to identify causal relationships, then uses Fourier transform surrogates to distinguish linear from nonlinear contributions. The motivation is that correlation can reflect linear causality well while missing nonlinear dependencies, potentially understating how strongly markets influence one another.

The authors report significant nonlinear causality between stock indices in Germany and the United States. They discuss how measuring both forms of causality could support market signal research, pair trading, and portfolio risk management, including the possibility of early warning signals for abnormal behavior. These findings motivate further applications rather than establish that such signals reliably improve trading outcomes. The evidence described is specific to the indices examined, and the excerpt does not provide details on the sample, robustness checks, or practical performance of strategies built from the measures.

Key ideas

• Pearson correlation captures linear dependence but can miss nonlinear relationships.
• The framework combines transfer entropy and convergent cross-mapping with surrogate analysis.
• The study reports nonlinear causality between German and U.S. stock indices.
• Causality measures may inform pair trading, signal research, and portfolio risk management.
• The excerpt does not establish the trading performance of strategies based on these measures.

Tags

# Linear and nonlinear causality in financial markets


# Linear and nonlinear causality in financial markets









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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

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