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Linearity is a system property characterized by a direct input-output relationship, combining homogeneity and additivity.
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Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
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Linear and nonlinear causality in financial markets.

Haochun Ma1,2, Davide Prosperino1,2, Alexander Haluszczynski2

  • 1Department of Physics, Ludwig-Maximilians-Universität München, Schellingstraße 4, Munich 80799, Germany.

Chaos (Woodbury, N.Y.)
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Summary
This summary is machine-generated.

Financial markets exhibit significant nonlinear causality, which traditional linear correlation measures overlook. This study introduces a framework to quantify nonlinear causality for improved trading and risk management.

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Area of Science:

  • Quantitative Finance
  • Financial Econometrics
  • Complex Systems Analysis

Background:

  • Accurate assessment of financial instrument co-dependence is crucial but challenging.
  • Traditional linear measures like Pearson correlation have limited explanatory power for complex market dynamics.

Purpose of the Study:

  • To develop a general framework for assessing linear and nonlinear co-dependencies in financial markets.
  • To identify and quantify linear and nonlinear causalities using advanced causal inference methods.

Main Methods:

  • Utilized transfer entropy and convergent cross-mapping for causal inference.
  • Employed Fourier transform surrogates to differentiate linear and nonlinear causality contributions.
  • Applied the framework to German and U.S. stock indices.

Main Results:

  • Significant nonlinear causality was detected in stock indices.
  • Pearson correlation underestimates true causality by ignoring nonlinear effects.
  • The framework successfully measures nonlinear causality and the correlation-causality fallacy.

Conclusions:

  • Nonlinear causality is a significant factor in financial markets, necessitating advanced analytical approaches.
  • The developed framework offers a more comprehensive understanding of financial market co-dependencies.
  • Identified linear and nonlinear causality can serve as early warning indicators for market anomalies and inform risk management strategies.