Granger Causality and Transfer Entropy for Financial Returns

E.M. Syczewskaa and Z.R. Struzikb,c,d aWarsaw School of Economics, Department of Economic Analyses, Institute of Econometrics, Madalińskiego 6/8, 02-513 Warsaw, Poland bRIKEN Brain Science Institute, 2-1 Hirosawa, Wako-shi 351-0198, Japan cGraduate School of Education, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan dInstitute of Theoretical Physics and Astrophysics, The University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland

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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.

DOI: 10.12693/APhysPolA.127.A-129 PACS numbers: 89.20.-a, 89.70.Cf, 02.50.-r, 05.45.Tp, 02.70.Rr