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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. [ABSTRACT FROM AUTHOR]

Financial contagion refers to the spread of market turmoils, for example from one country or index to another country or another index. It is standardly assessed by modelling the evolution of the correlation matrix, for example of returns, usually after removing univariate dynamics with the GARCH model. However, significant events like crises visible in one financial market are usually reflected in other financial markets/countries simultaneously in several dimensions, i.e., in general, entire distributions of returns in other markets are affected. These distributions are determined/described by their expected value, variance, skewness, kurtosis and other statistics that determine the shape of the distribution function of returns, which can be based on higher (mixed) moments. These descriptive statistics are not constant over time, and, moreover, they can interreact within the given market and among the markets over time. In this article we propose, and use for the daily values of five indexes (CAC40, DAX30, DJIA, FTSE250 and WIG20) over the time period 2006–2017, a new, simple and computationally inexpensive methodology to automatically extend contagion evaluation from the evolution of the correlation matrix to the evolution of multiple higher mixed moments as well. Specifically, the joint distribution of normalized variables for each pair of indexes is modeled as a polynomial with time evolving coefficients estimated using an exponential moving average. As we can obtain any arbitrary number of evolving mixed moments this way, its dimensionality reduction using PCA (principal component analysis) is also discussed, obtaining a lower number of dominating and relatively independent features, which can each be interpreted through a polynomial that describes the corresponding perturbation of joint distribution. We obtain features that describe the interrelations among stock markets in several dimensions and that provide information about the current stage of crisis and the strength of the contagion process. [ABSTRACT FROM AUTHOR]

This paper is concerned with a dependence analysis of returns, return volatility and trading volume for five companies listed on the Vienna Stock Exchange and five from theWarsaw Stock Exchange. Taking into account high frequency data for these companies, tests based on a comparison of Bernstein copula densities using the Hellinger distance were conducted. The paper presents some patterns of causal and other relationships between stock returns, realized volatility and expected and unexpected trading volume. There is a linear causality running fromrealized volatility to expected trading volume, and a lack of nonlinear dependence in the opposite direction. The authors detected strong linear and nonlinear causality from stock returns to expected trading volume. They did not find causality running in the opposite direction. In addition, the existence of fractional cointegration was examined. Despite the equality of the long memory parameters of realized volatility and trading volumes, they do not move together in the long term horizon. [ABSTRACT FROM AUTHOR]

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