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Entropy 2013, 15(7), 2635-2661; doi:10.3390/e15072635

Simulation Study of Direct Causality Measures in Multivariate Time Series

1,* , 1,2
1 Department of Economics, University of Macedonia, Egnatias 156, 54006, Thessaloniki, Greece 2 University of Strasbourg, BETA, University of Paris 10, Economix, ISC-Paris, Ile-de-France, France 3 Faculty of Engineering, Aristotle University of Thessaloniki, University Campus, 54124, Thessaloniki, Greece 4 Faculty of Economics, Department of Economics and Econometrics, University of Amsterdam, Valckenierstraat 65-67, 1018 XE, Amsterdam, The Netherlands
* Author to whom correspondence should be addressed.
Received: 28 March 2013 / Revised: 5 June 2013 / Accepted: 27 June 2013 / Published: 4 July 2013
(This article belongs to the Special Issue Transfer Entropy)
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Measures of the direction and strength of the interdependence among time series from multivariate systems are evaluated based on their statistical significance and discrimination ability. The best-known measures estimating direct causal effects, both linear and nonlinear, are considered, i.e., conditional Granger causality index (CGCI), partial Granger causality index (PGCI), partial directed coherence (PDC), partial transfer entropy (PTE), partial symbolic transfer entropy (PSTE) and partial mutual information on mixed embedding (PMIME). The performance of the multivariate coupling measures is assessed on stochastic and chaotic simulated uncoupled and coupled dynamical systems for different settings of embedding dimension and time series length. The CGCI, PGCI and PDC seem to outperform the other causality measures in the case of the linearly coupled systems, while the PGCI is the most effective one when latent and exogenous variables are present. The PMIME outweighs all others in the case of nonlinear simulation systems.
Keywords: direct Granger causality; multivariate time series; information measures direct Granger causality; multivariate time series; information measures
This is an open access article distributed under the Creative Commons Attribution License (CC BY) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Papana, A.; Kyrtsou, C.; Kugiumtzis, D.; Diks, C. Simulation Study of Direct Causality Measures in Multivariate Time Series. Entropy 2013, 15, 2635-2661.

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