Causalities and their Drivers in Synthetic and Financial Data

Abstract

Identifying and describing the dynamics of complex systems is a central challenge in various areas of science, such as physics, finance, or climatology. Here, we analyze the causal structure of chaotic systems using Fourier transform surrogates that enables us to identify the different (linear and nonlinear) causality drivers. We further show that a simple rationale and calibration algorithm are sufficient to extract the governing equations directly from the causal structure of the data. We demonstrate the applicability of the framework to real-world dynamical systems using financial data (stock indices from Europe, United States, China, Emerging Markets, Japan and Pacific excluding Japan) before and after the COVID-19 outbreak. It turns out that the pandemic triggered a fundamental rupture in the world economy, which is reflected in the causal structure and the resulting equations. Specifically, nonlinear causal relations have significantly increased in the global financial market after the COVID-19 outbreak [1]. Further differential analyses revealed that that the 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, underestimates causality itself [2]. The presented framework enables the measurement of nonlinear causality and motivates methods for inferring market signals, quantifying portfolio risk, and constructing less risky portfolios. Our model suggests that nonlinear causality can be used as an early warning indicator of abnormal market behavior, allowing for more accurate risk management and better portfolio construction. [1] H. Ma, A. Haluszczynski, D. Prosperino & C. Räth, Identifying causality drivers and deriving governing equations of nonlinear complex systems, Chaos, 32, 103128 (2022) [2] H. Ma, D. Prosperino, A. Haluszczynski & C. Räth, Linear and nonlinear causality in financial markets (submitted)