The aim of this study is to assess and compare changes in regularity in the 36 European and the U.S. stock market indices within major turbulence periods. Two periods are investigated: the Global Financial Crisis in 2007–2009 and the COVID-19 pandemic outbreak in 2020–2021. The proposed research hypothesis states that entropy of an equity market index decreases during turbulence periods, which implies that regularity and predictability of a stock market index returns increase in such cases. To capture sequential regularity in daily time series of stock market indices, the Sample Entropy algorithm (SampEn) is used. Changes in the SampEn values before and during the particular turbulence period are estimated. The empirical findings are unambiguous and confirm no reason to reject the research hypothesis. Moreover, additional formal statistical analyses indicate that the SampEn results are similar both for developed and emerging European economies. Furthermore, the rolling-window procedure is utilized to assess the evolution of SampEn over time.

One of the crucial steps in the multi-criteria decision analysis involves establishing the importance of criteria and determining the relationship between them. This paper proposes an extended Hellwig’s method (H_EM) that utilizes entropy-based weights and Mahalanobis distance to address this issue. By incorporating the concept of entropy, weights are determined based on their information content represented by the matrix data. The Mahalanobis distance is employed to address interdependencies among criteria, contributing to the improved performance of the proposed framework. To illustrate the relevance and effectiveness of the extended H_EM method, this study utilizes it to assess the progress toward achieving Sustainable Development Goal 4 of the 2030 Agenda within the European Union countries for education in the year 2021. Performance comparison is conducted between results obtained by the extended Hellwig’s method and its other variants. The results reveal a significant impact on the ranking of the EU countries in the education area, depending on the choice of distance measure (Euclidean or Mahalanobis) and the system of weights (equal or entropy-based). Overall, this study highlights the potential of the proposed method in addressing complex decision-making scenarios with interdependent criteria.

The main goal of this paper is a quantitative identification of bear market periods during the 2007–2009 global financial crisis in the case of the Visegrad Group stock markets. We analyse four countries, namely Poland, the Czech Republic, Hungary, and Slovakia and, for comparison, the US stock market. The sample period begins on May1, 2004, and ends on April 30, 2013, i.e. it includes the 2007 US subprime crisis. We use the statistical method of dividing market states into bullish and bearish markets. Our results reveal October 2007–February 2009 as the common downmarket period of the recent global financial crisis, except for Slovakia. It is instructive to formally identify crises, as it enables sensitivity analyses of various relationships and linkages among international stock markets using econometric and statistical tools, with respect to the pre-, post- and crisis periods. Moreover, we investigate the effect of increasing cross-market correlations in the crisis compared to the pre-crisis period, applying both standard contemporaneous correlations and volatility-adjusted correlation coefficients. The results confirm that accommodating heteroskedasticity is critical for detecting contagion across economies. A number of studies document that crossmarket correlations vary over time, thereby making the benefits of international portfolio choice and diversification questionable.

The main goal of this paper is a direct identification of crisis periods on the eight Central and Eastern European (CEE) stock markets, and, for comparison, on the U.S. market. We employ a statistical procedure of dividing market states into up and down markets. Our aim is to examine whether crisis periods are common in various countries, and the results confirm Oct 2007 – Feb 2009 as the common period of the recent global financial crisis, except for Slovakia. Moreover, we investigate the effect of increasing cross–market correlations in the crisis period in the context of contagion, applying both standard contemporaneous correlations and volatility-adjusted correlation coefficients. Our results confirm that accommodating heteroskedasticity is crucial for detecting contagion across stock markets. The data consists of monthly logarithmic returns of the major CEE and the U.S. stock market indexes, in the period May 2004 – April 2013

Sustainable Cities and Communities within the European Union (EU) are crucial for achieving Sustainable Development Goal (SDG) 11, which aims to make cities and human settlements inclusive, safe, resilient, and sustainable. This goal is particularly pertinent to the EU due to challenges such as urbanization, climate change, infrastructure demands, transport issues, and natural resource management. The implementation of SDG 11 across Europe shows varying levels of success among countries and regions, highlighting the need for tailored, local strategies for sustainable urban development. The primary goal of this paper is to employ the Multi-Criteria Method Integrating Distances to Ideal and Anti-Ideal Points to determine the Sustainable Cities and Communities Index (SCCI). Using Eurostat data, this method provides a comprehensive evaluation and ranking of EU countries based on their performance in achieving SDG 11 in EU countries in 2015 and 2020. By integrating various indicators related to urban sustainability—such as access to public transport, air quality, land use, and housing conditions—the SCCI offers a nuanced understanding of how different countries perform relative to one another. The SCCI facilitates the identification of best practices and areas requiring improvement by comparing each country’s performance to ideal and anti-ideal points. This comparison allows policymakers to develop more targeted and effective strategies. Additionally, it highlights disparities between countries and regions, which is essential for fostering regional cooperation and ensuring equitable progress towards sustainable urban development across the EU. This study confirmed significant disparities among EU countries in the realization of SDG 11 in 2015 and 2020, revealing that Italy achieved the most substantial progress, while Spain experienced the greatest regress during the analyzed period.

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