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Linear and nonlinear causality in financial markets (2312.16185v1)

Published 18 Dec 2023 in q-fin.ST and physics.data-an

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.

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Summary

  • The paper introduces a dual-method framework that distinguishes linear from nonlinear causal relationships in financial markets using Transfer Entropy and Convergent Cross-Mapping.
  • It demonstrates that conventional measures like Pearson correlation overlook significant nonlinear market dependencies identified via Fourier transform surrogates.
  • The study shows that integrating causal measures can serve as early warning indicators for market volatility, improving trading strategies and risk management.

Linear and Nonlinear Causality in Financial Markets

The paper "Linear and Nonlinear Causality in Financial Markets" presents a comprehensive framework for identifying and quantifying co-dependencies among financial instruments, with a focus on both linear and nonlinear causal relationships. This research is particularly significant given the limitations of traditional linear measures, such as the Pearson correlation, which have long been used in financial markets to explain asset co-dependence. The insufficiency of these linear measures in capturing the full spectrum of market dynamics necessitates more sophisticated approaches.

At the core of this research are two causal inference methodologies: Transfer Entropy (TE) and Convergent Cross-Mapping (CCM). Both methods are employed to measure causal relationships, with Fourier transform surrogates used to separate the linear from the nonlinear components. This distinction is crucial as it highlights the potential oversight of significant nonlinear dependencies by conventional linear measures.

The authors apply their framework to major German and U.S. stock indices, uncovering substantial nonlinear causalities which have been largely underestimated in previous analyses. This reveals an important insight: that correlation serves as a good proxy merely for linear causality and neglects the nonlinear effects that are fundamental to an accurate understanding of financial markets. By incorporating causality into their analysis, the authors provide a more nuanced approach, emphasizing the correlation-causality fallacy and its implications for market interpretation.

The authors further reveal that both linear and nonlinear causality can be instrumental as early warning indicators of abnormal market behavior. This has practical implications, suggesting that more effective trading strategies and improved risk management of portfolios can be achieved by integrating these measures. For instance, during significant economic events such as the dotcom bubble burst and the 2008 financial crisis, the nonlinear contribution to market dynamics becomes more pronounced. By continuously monitoring these causal measures, practitioners can better anticipate and respond to potential market disruptions.

The paper not only offers an innovative approach to understanding market dynamics but also proposes tangible applications, including market signal inference, pair trading, and portfolio optimization. The authors demonstrate that incorporating these causality measures into traditional financial models can lead to better performance outcomes. Particularly in pair trading and portfolio optimization scenarios, causality measures provide a more robust framework compared to traditional reliance on Pearson correlation alone.

In conclusion, the framework outlined in this paper sheds light on the complexity of financial market interactions by presenting a clear method to distinguish between linear and nonlinear causalities. As the financial landscape continues to evolve, the proposed methodologies offer promising avenues for future research, potentially leading to the development of advanced trading algorithms and enhanced prediction models. While this paper is oriented towards identifying causal relationships, its broader implications can contribute to an improved theoretical understanding of market dynamics, offering a richer context for financial decision-making and risk management.

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