The hidden nature of causality is a puzzling, yet critical notion for effective decision-making. Financial markets are characterized by fluctuating interdependencies which seldom give rise to emergent phenomena such as bubbles or crashes. In this paper, we propose a method based on symbolic dynamics, which probes beneath the surface of abstract causality and unveils the nature of causal interactions. Our method allows distinction between positive and negative interdependencies as well as a hybrid form that we refer to as “dark causality.” We propose an algorithm which is validated by models of a priori defined causal interaction. Then, we test our method on asset pairs and on a network of sovereign credit default swaps (CDS). Our findings suggest that dark causality dominates the sovereign CDS network, indicating interdependencies which require caution from an investor’s perspective.

Through financial network analysis we ascertain the existence of important causal behavior among certain financial assets, as inferred by eight different causality methods. To our knowledge this is the first extensive comparative analysis of financial networks as produced by various causality methods. Additionally, some specific nonlinear causalities are used for the first time in the financial network research. Our results contradict the Efficient Market Hypothesis and open new horizons for further investigation and possible arbitrage opportunities. Moreover, we find some evidence that two of the causality methods used, at least to some extent, could warn us about the financial crisis of 2007-2009. Furthermore, we test the similarity percentage of the eight causality methods and we find that the most similar pair of causality-induced networks is on average less than 50% similar throughout the time period examined, rendering thus the comparability and substitutability among those causality methods rather dubious. We also rank the assets in terms of overall out-strength centrality and we find that there is an underlying bonds regime almost monopolising in some cases the realm of causality. Finally, using the network visualization, we observe an established pattern (i.e., across all causalities) of oil's rising role as the financial network faces the Chinese stock market crash.

Throughout time, operational laws and concepts from complex systems have been employed to quantitatively model important aspects and interactions in nature and society. Nevertheless, it remains enigmatic and challenging, yet inspiring, to predict the actual interdependencies that comprise the structure of such systems, particularly when the causal interactions observed in real-world phenomena might be persistently hidden. In this article, we propose a robust methodology for detecting the latent and elusive structure of dynamic complex systems. Our treatment utilizes short-term predictions from information embedded in reconstructed state space. In this regard, using a broad class of real-world applications from ecology, neurology, and finance, we explore and are able to demonstrate our method’s power and accuracy to reconstruct the fundamental structure of these complex systems, and simultaneously highlight their most fundamental operations.

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