Mutual information between Polish subindexes – the use of copula entropy around the time of the COVID-19 pandemic

Henryk Gurgul; Robert Syrek

doi:https://doi.org/10.59170/stattrans-2024-002

Mutual information between Polish subindexes – the use of copula entropy around the time of the COVID-19 pandemic

Henryk Gurgul Department of Applications of Mathematics in Economics, AGH University of Science and Technology in Cracow, Poland ORCID:https://orcid.org/0000-0002-6192-2995 , Robert Syrek Institute of Economics, Finance and Management, Jagiellonian University in Cracow, Poland ORCID:https://orcid.org/0000-0002-8212-8248 Statistics in Transition new series, vol. 25, 2024, 1, pages: 23-41 Published online: 6 March 2024 https://doi.org/10.59170/stattrans-2024-002 Citation: Gurgul, H., Syrek, R., 2024. Mutual information between Polish subindexes – the use of copula entropy around the time of the COVID-19 pandemic. Statistics in Transition new series, 25(1), pp. 23-41. https://doi.org/10.59170/stattrans-2024-002.

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ABSTRACT

In this paper, the copula theory is used to describe the dependence structure between variables, while the information theory provides the tools necessary to measure the uncertainty associated with these variables. What both theories have in common is copula entropy, which is strictly related to mutual information.
The findings of this study, focusing on the dependence of the (sub)indexes of the Polish stock market during the pandemic period, may prove useful not only to investors from Poland, but also from other countries, especially Central European, in making investment decisions.
The results of calculating the interdependencies between WIG, sectoral indexes and among sectoral indexes of the Polish economy using copula entropy and Pearson’s correlation are quite different.
The source of the basic difference between copula entropy and Pearson’s correlation is that the former enables the measurement of nonlinear interdependencies, while the latter not. The interrelations on the stock markets are nonlinear and returns are not normally distributed in general. The use of copulas is also superior in terms of ranking correlation, as it is more general and allows the examination of the structure of dependencies between extreme values.

KEYWORDS

Polish subindexes, COVID-19 pandemic, mutual information, copula entropy.

JEL

G15, G19

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