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.
A b s t r a c t. In this paper the possible interdependence between bilateral exchange rate behavior and the corresponding stock indices is checked, with application to the EURPLN rate and the DAX and WIG20 stock indices. Methods and results are similar to previous study of USDPLN exchange rate, and SP500 and WIG20 indices.
The aim of the paper is to present an example of analysis of exchange rate behavior with use of tools, built in GRETL econometric package, which have been developed by researchers often with background in physics or similar fields, but some (such as tests of integration and cointegration) are less known to physical audience. The series of interest is a bilateral USDPLN exchange rate; including the corresponding stock indices as additional variables can improve quality of a model even in period of crisis.
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