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Granger Causality and Transfer Entropy for Financial Returns

100%
Syczewska E., Struzik Z.
Acta Physica Polonica A
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2015
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vol. 127
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issue 3A
A-129-A-135
EN
Granger causality in its linear form has been shown by Barnett, Barrett and Seth [Phys. Rev. Lett. 103, 238701 (2009)] to be equivalent to transfer entropy in case of Gaussian distribution. Generalizations by Hlaváčková-Schindler [Appl. Math. Sci. 5, 3637 (2011)] are applied to distributions typical for biomedical applications. The financial returns, which are of great importance in financial econometrics, typically do not have Gaussian distribution. Generalizations leading to the concept of nonlinear Granger causality (e.g. causality in variance, causality in risk), known and applied in econometric literature, seem to be less known outside this field. In the paper an overview of some of the definitions and applications is given. In particular, we indicate some recent econometric results concerning application of the tests in linear multivariate framework. We emphasize importance of other variants of Granger causality, and need of development of methods reflecting features of financial variables.
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Dynamic Structural and Topological Phase Transitions on the Warsaw Stock Exchange: A Phenomenological Approach

81%
Sienkiewicz A., Gubiec T., Kutner R., Struzik Z.
Acta Physica Polonica A
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2013
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vol. 123
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issue 3
615-620
EN
We study crash dynamics of the Warsaw Stock Exchange by using minimal spanning tree networks. We identify the transition of the complex network during its evolution from a (hierarchical) power law minimal spanning tree network - representing the stable state of Warsaw Stock Exchange before the recent worldwide financial crash, to a superstar-like (or superhub) minimal spanning tree network of the market decorated by a hierarchy of trees - an unstable, intermediate market state. Subsequently, we observe a transition from this complex tree to the topology of the (hierarchical) power law minimal spanning tree network decorated by several star-like trees or hubs - this structure and topology represent the Warsaw Stock Exchange after the worldwide financial crash, and can be considered to be an aftershock. Our results can serve as an empirical foundation for a future theory of dynamic structural and topological phase transitions on financial markets.
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