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Detecting Nonlinear Interactions in Complex Systems: Application in Financial Markets

Authors :
Akylas Fotiadis
Ioannis Vlachos
Dimitris Kugiumtzis
Source :
Entropy, Vol 25, Iss 2, p 370 (2023)
Publication Year :
2023
Publisher :
MDPI AG, 2023.

Abstract

Emerging or diminishing nonlinear interactions in the evolution of a complex system may signal a possible structural change in its underlying mechanism. This type of structural break may exist in many applications, such as in climate and finance, and standard methods for change-point detection may not be sensitive to it. In this article, we present a novel scheme for detecting structural breaks through the occurrence or vanishing of nonlinear causal relationships in a complex system. A significance resampling test was developed for the null hypothesis (H0) of no nonlinear causal relationships using (a) an appropriate Gaussian instantaneous transform and vector autoregressive (VAR) process to generate the resampled multivariate time series consistent with H0; (b) the modelfree Granger causality measure of partial mutual information from mixed embedding (PMIME) to estimate all causal relationships; and (c) a characteristic of the network formed by PMIME as test statistic. The significance test was applied to sliding windows on the observed multivariate time series, and the change from rejection to no-rejection of H0, or the opposite, signaled a non-trivial change of the underlying dynamics of the observed complex system. Different network indices that capture different characteristics of the PMIME networks were used as test statistics. The test was evaluated on multiple synthetic complex and chaotic systems, as well as on linear and nonlinear stochastic systems, demonstrating that the proposed methodology is capable of detecting nonlinear causality. Furthermore, the scheme was applied to different records of financial indices regarding the global financial crisis of 2008, the two commodity crises of 2014 and 2020, the Brexit referendum of 2016, and the outbreak of COVID-19, accurately identifying the structural breaks at the identified times.

Details

Language :
English
ISSN :
10994300
Volume :
25
Issue :
2
Database :
Directory of Open Access Journals
Journal :
Entropy
Publication Type :
Academic Journal
Accession number :
edsdoj.9dc56c2beeed414bbd8a0b2cf7f4b191
Document Type :
article
Full Text :
https://doi.org/10.3390/e25020370