Mutual information matrix based on asymmetric Shannon entropy for nonlinear interactions of time series

Contreras-Reyes, Javier E.

doi:10.1007/s11071-021-06498-w

Cited by 22 publications

(8 citation statements)

References 33 publications

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“…The high Shannon entropy values (greater than 1.0) mentioned for the time series data of the coupled pendulum system are consistent with the observed chaotic dynamics. For chaotic systems, the Shannon entropy is expected to be high due to the inherent unpredictability and lack of regularity in the system's behavior [39].…”

Section: Resultsmentioning

confidence: 99%

Reappraising Double Pendulum Dynamics across Multiple Computational Platforms

Herho,

Fajary,

Herho

et al. 2024

Preprint

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This study presents the complexity and sensitivity of chaotic system dynamics in the case of the double pendulum. It applied detailed numerical analyses of the double pendulum in multiple computing platforms in order to demonstrate the complexity in behavior of the system of double pendulums. The equations of motion were derived from the Euler-Lagrange formalism, in order to capture the system's dynamics, which is coupled nonlinearly. These were solved numerically using the efficient Runge-Kutta-Fehlberg method, implemented in Python, R, GNU Octave, and Julia, while runtimes and memory usage were extensively benchmarked across these environments. Time series analyses, including the calculation of Shannon entropy and the Kolmogorov-Smirnov test, quantified the system's unpredictability and sensitivity to infinitesimal perturbations of the initial conditions. Phase space diagrams illustrated the intricate trajectories and strange attractors, as further confirmation of the chaotic nature of the double pendulum. All the findings have a clear indication of the importance of accurate measurements of the initial condition in a chaotic system, contributing to an increased understanding of nonlinear dynamics. Future research directions are faster simulations using Numba and GPU computing, stochastic effects, chaotic synchronization, and applications in climate modeling. This work will be useful for understanding chaos theory and efficient computational approaches in complex systems of dynamical nature.

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Section: Resultsmentioning

confidence: 99%

Reappraising Double Pendulum Dynamics across Multiple Computational Platforms

Herho,

Fajary,

Herho

et al. 2024

Preprint

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“…So, the total probability of contributions in predicting a target is one. The entropy is calculated as [ 25 ], where F ij is the element of the feature ranking matrix F at row i and column j . The entropy will be at its highest value when the indices influence each other equally.…”

Section: Resultsmentioning

confidence: 99%

Feature ranking and network analysis of global financial indices

2022

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The feature ranking method of machine learning is applied to investigate the feature ranking and network properties of 21 world stock indices. The feature ranking is the probability of influence of each index on the target. The feature ranking matrix is determined by using the returns of indices on a certain day to predict the price returns of the next day using Random Forest and Gradient Boosting. We find that the North American indices influence others significantly during the global financial crisis, while during the European sovereign debt crisis, the significant indices are American and European. The US stock indices dominate the world stock market in most periods. The indices of two Asian countries (India and China) influence remarkably in some periods, which occurred due to the unrest state of these markets. The networks based on feature ranking are constructed by assigning a threshold at the mean of the feature ranking matrix. The global reaching centrality of the threshold network is found to increase significantly during the global financial crisis. Finally, we determine Shannon entropy from the probabilities of influence of indices on the target. The sharp drops of entropy are observed during big crises, which are due to the dominance of a few indices in these periods that can be used as a measure of the overall distribution of influences. Through this technique, we identify the indices that are influential in comparison to others, especially during crises, which can be useful to study the contagions of the global stock market.

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“…Mutual information is used as a generalized correlation measure that quantifies nonlinear associations [ 65 , 66 ]. Mutual information is also considered to form the Mutual Information Matrix for the study of nonlinear interactions in multivariate time series [ 67 ]. Time-delayed mutual information takes into account the lag difference of the variables [ 65 ].…”

Section: Non-directional Connectivity Measuresmentioning

confidence: 99%

Connectivity Analysis for Multivariate Time Series: Correlation vs. Causality

Papana

2021

Entropy

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The study of the interdependence relationships of the variables of an examined system is of great importance and remains a challenging task. There are two distinct cases of interdependence. In the first case, the variables evolve in synchrony, connections are undirected and the connectivity is examined based on symmetric measures, such as correlation. In the second case, a variable drives another one and they are connected with a causal relationship. Therefore, directed connections entail the determination of the interrelationships based on causality measures. The main open question that arises is the following: can symmetric correlation measures or directional causality measures be applied to infer the connectivity network of an examined system? Using simulations, we demonstrate the performance of different connectivity measures in case of contemporaneous or/and temporal dependencies. Results suggest the sensitivity of correlation measures when temporal dependencies exist in the data. On the other hand, causality measures do not spuriously indicate causal effects when data present only contemporaneous dependencies. Finally, the necessity of introducing effective instantaneous causality measures is highlighted since they are able to handle both contemporaneous and causal effects at the same time. Results based on instantaneous causality measures are promising; however, further investigation is required in order to achieve an overall satisfactory performance.

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Mutual information matrix based on asymmetric Shannon entropy for nonlinear interactions of time series

Cited by 22 publications

References 33 publications

Reappraising Double Pendulum Dynamics across Multiple Computational Platforms

Reappraising Double Pendulum Dynamics across Multiple Computational Platforms

Feature ranking and network analysis of global financial indices

Connectivity Analysis for Multivariate Time Series: Correlation vs. Causality

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