Mutual information between the main foreign subindices: The application of copula entropy around WHO’s declaration date at the time of the COVID-19 pandemic

Abstract

Objective: The objective of this article is to investigate the dependencies between selected European subindices before and during the COVID-19 pandemic.

Research Design & Methods: The main analysis was quantitative. We used copula entropy and Pearson’s correlation. We considered the closing prices of sectoral indices from France (CAC sectors), Germany (DAX sectors), the UK (FTSE sectors), and the US (SP sectors), along with the main indices from these countries, that is CAC40, DAX, SP500, and FTSE100 (we collected the data from the database investing.com for the period from 4 January 2017 to 30 March 2023). We performed all analyses using R along with supplementary packages.

Findings: When it comes to indications of the strength of dependence before and after the event (the outbreak of the COVID-19 pandemic) in relation to mutual information (delta) and linear correlation, we saw the biggest differences for the German market. For the DAX sectors, linear correlation underestimates post-event dependencies. The dependencies for other countries were similar on average. For half of the sectors (all markets), we recorded an increase in dependence after the event. A sector where we recorded growth in all countries was the TECH sector.

Implications & Recommendations: The dependence measurement using mutual information expressed in terms of copulas has many advantages. It is not limited to measuring linear correlations. It can also capture a nonlinear correlation. Furthermore, it not only measures the dependence degree, but also considers the dependence structure, which is more than a correlation. Moreover, there was no assumption about the ellipticity of marginal and joint distribution. This dependence measure even allows for the modelling of the dependence of variables with different cumulative distribution functions.

Contribution & Value Added: The novelty of this article is that it compares the results of dependence measurements by linear correlations and mutual information expressed in terms of copula entropy. Considering the indices and subindices of the main European stock markets, when both measures of dependence were used, we obtained significantly different results in both subperiods under investigation (i.e. before and after March 11, 2020).

Keywords

foreign main subindices, pandemic Covid-19, mutual information, copula entropy, linear correlation

Author Biography

Henryk Gurgul

Professor at AGH University of Science and Technology in Krakow, Department of Applications of Mathematics in Economics. His research interests include econometrics, financial econometrics, international financial markets, and input-output models. Author of more than 200 publications. Visiting professor at universities in Graz and Klagenfurt (Austria), Erlangen-Nuernberg, Greifswald, Ilmenau, Saarbruecken (Germany), Trieste and Siena (Italy), Valencia (Spain), Koper (Slovenia), Joensuu (Finland). Honours: Awarded in 2007 the most prestigious prize for economics in Poland Bank Handlowy w Warszawie S.A. Award (Citi Bank), in 2015 awarded the Medal of Honour, University of Graz, Austria.

Robert Syrek

PhD, Assistant Professor at the Institute of Economics, Finance and Management, Faculty of Management and Social Communication at the Jagiellonian University in Krakow. His main areas of research interest include time series analysis and forecasting, financial econometrics and modelling the dependence structures of financial time series (especially using copula functions).

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