Correlation Dimension Detects Causal Links in Coupled Dynamical Systems

It is becoming increasingly clear that causal analysis of dynamical systems requires different approaches than, for example, causal analysis of interconnected autoregressive processes. In this study, a correlation dimension estimated in reconstructed state spaces is used to detect causality. If dete...

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Bibliographic Details
Published in:Entropy (Basel, Switzerland) Switzerland), 2019-08, Vol.21 (9), p.818
Main Author: Krakovská, Anna
Format: Article
Language:English
Subjects:
Autoregressive processes
Causality
Chaos theory
common driver
correlation dimension
Dynamical systems
Fractals
Methods
the arrow of time
Time series
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Summary:It is becoming increasingly clear that causal analysis of dynamical systems requires different approaches than, for example, causal analysis of interconnected autoregressive processes. In this study, a correlation dimension estimated in reconstructed state spaces is used to detect causality. If deterministic dynamics plays a dominant role in data then the method based on the correlation dimension can serve as a fast and reliable way to reveal causal relationships between and within the systems. This study demonstrates that the method, unlike most other causal approaches, detects causality well, even for very weak links. It can also identify cases of uncoupled systems that are causally affected by a hidden common driver.
ISSN:1099-4300
1099-4300
DOI:10.3390/e21090818