Editorial

3 pages, 168 KiB

Open AccessEditorial

Entropy-Based Applications in Economics, Finance, and Management

by Joanna Olbryś

Entropy 2022, 24(10), 1468; https://doi.org/10.3390/e24101468 - 14 Oct 2022

Cited by 1 | Viewed by 1229

The concept of entropy originated from physics (precisely, from thermodynamics), but it has been utilized in many research fields to characterize the complexity of a system and to investigate the information content of a probability distribution [...] Full article

(This article belongs to the Special Issue Entropy-Based Applications in Economics, Finance, and Management)

Research

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22 pages, 12853 KiB

Open AccessArticle

Regularity in Stock Market Indices within Turbulence Periods: The Sample Entropy Approach

by Joanna Olbryś and Elżbieta Majewska

Entropy 2022, 24(7), 921; https://doi.org/10.3390/e24070921 - 01 Jul 2022

Cited by 8 | Viewed by 1381

Abstract

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 [...] Read more.

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. Full article

(This article belongs to the Special Issue Entropy-Based Applications in Economics, Finance, and Management)

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32 pages, 18172 KiB

Open AccessEditor’s ChoiceArticle

Causal Inference in Time Series in Terms of Rényi Transfer Entropy

by Petr Jizba, Hynek Lavička and Zlata Tabachová

Entropy 2022, 24(7), 855; https://doi.org/10.3390/e24070855 - 22 Jun 2022

Cited by 4 | Viewed by 2756

Abstract

Uncovering causal interdependencies from observational data is one of the great challenges of a nonlinear time series analysis. In this paper, we discuss this topic with the help of an information-theoretic concept known as Rényi’s information measure. In particular, we tackle the directional [...] Read more.

Uncovering causal interdependencies from observational data is one of the great challenges of a nonlinear time series analysis. In this paper, we discuss this topic with the help of an information-theoretic concept known as Rényi’s information measure. In particular, we tackle the directional information flow between bivariate time series in terms of Rényi’s transfer entropy. We show that by choosing Rényi’s parameter

α

, we can appropriately control information that is transferred only between selected parts of the underlying distributions. This, in turn, is a particularly potent tool for quantifying causal interdependencies in time series, where the knowledge of “black swan” events, such as spikes or sudden jumps, are of key importance. In this connection, we first prove that for Gaussian variables, Granger causality and Rényi transfer entropy are entirely equivalent. Moreover, we also partially extend these results to heavy-tailed

α

-Gaussian variables. These results allow establishing a connection between autoregressive and Rényi entropy-based information-theoretic approaches to data-driven causal inference. To aid our intuition, we employed the Leonenko et al. entropy estimator and analyzed Rényi’s information flow between bivariate time series generated from two unidirectionally coupled Rössler systems. Notably, we find that Rényi’s transfer entropy not only allows us to detect a threshold of synchronization but it also provides non-trivial insight into the structure of a transient regime that exists between the region of chaotic correlations and synchronization threshold. In addition, from Rényi’s transfer entropy, we could reliably infer the direction of coupling and, hence, causality, only for coupling strengths smaller than the onset value of the transient regime, i.e., when two Rössler systems are coupled but have not yet entered synchronization. Full article

(This article belongs to the Special Issue Entropy-Based Applications in Economics, Finance, and Management)

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17 pages, 507 KiB

Open AccessArticle

Role of Age and Education as the Determinant of Income Inequality in Poland: Decomposition of the Mean Logarithmic Deviation

by Ewa Wędrowska and Joanna Muszyńska

Entropy 2022, 24(6), 773; https://doi.org/10.3390/e24060773 - 30 May 2022

Cited by 5 | Viewed by 1897

Abstract

Measures of inequality can be used to illustrate inequality between and within groups, but the choice of the appropriate measure can have different implications. This study focused on the Mean Logarithmic Deviation, the measure proposed by Theil and based on the techniques of [...] Read more.

Measures of inequality can be used to illustrate inequality between and within groups, but the choice of the appropriate measure can have different implications. This study focused on the Mean Logarithmic Deviation, the measure proposed by Theil and based on the techniques of statistical information theory. The MLD was selected because of its attractive properties: fulfillment of the principle of monotonicity and the possibility of additive decomposition. The following study objectives were formulated: (1) to assess the degree of inequality in the population and in the distinguished subgroups, (2) to determine the extent to which education and age influence the level of inequality, and (3) to ascertain what factors contribute to changes in the level of inequality in Poland. The study confirmed an association between the level of education and the average income of the groups distinguished on this basis. The education level of the household head remains an important determinant of household income inequality in Poland, despite the decline in the “educational bonus”. The study also found that differences in the age of the household head had a smaller effect on income inequality than the level of education. However, it can be concluded that the higher share of older people may contribute to an increase in income inequality between groups, as the income from pension in Poland is more homogeneous than the income from work in younger groups. Moreover, the current paper seeks to situate Theil’s approach in the context of scholarly writings since 1967. Full article

(This article belongs to the Special Issue Entropy-Based Applications in Economics, Finance, and Management)

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11 pages, 336 KiB

Open AccessArticle

Replication in Energy Markets: Use and Misuse of Chaos Tools

by Loretta Mastroeni and Pierluigi Vellucci

Entropy 2022, 24(5), 701; https://doi.org/10.3390/e24050701 - 16 May 2022

Cited by 4 | Viewed by 2064

Abstract

As pointed out by many researchers, replication plays a key role in the credibility of applied sciences and the confidence in all research findings. With regard, in particular, to energy finance and economics, replication papers are rare, probably because they are hampered by [...] Read more.

As pointed out by many researchers, replication plays a key role in the credibility of applied sciences and the confidence in all research findings. With regard, in particular, to energy finance and economics, replication papers are rare, probably because they are hampered by inaccessible data, but their aim is crucial. We consider two ways to avoid misleading results on the ostensible chaoticity of price series. The first one is represented by the proper mathematical definition of chaos and the related theoretical background, while the latter is represented by the hybrid approach that we propose here—i.e., consisting of considering the dynamical system underlying the price time series as a deterministic system with noise. We find that both chaotic and stochastic features coexist in the energy commodity markets, although the misuse of some tests in the established practice in the literature may say otherwise. Full article

(This article belongs to the Special Issue Entropy-Based Applications in Economics, Finance, and Management)

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19 pages, 2785 KiB

Open AccessArticle

Linear and Nonlinear Effects in Connectedness Structure: Comparison between European Stock Markets

by Renata Karkowska and Szczepan Urjasz

Entropy 2022, 24(2), 303; https://doi.org/10.3390/e24020303 - 21 Feb 2022

Cited by 5 | Viewed by 2079

Abstract

The purpose of this research is to compare the risk transfer structure in Central and Eastern European and Western European stock markets during the 2007–2009 financial crisis and the COVID-19 pandemic. Similar to the global financial crisis (GFC), the spread of coronavirus (COVID-19) [...] Read more.

The purpose of this research is to compare the risk transfer structure in Central and Eastern European and Western European stock markets during the 2007–2009 financial crisis and the COVID-19 pandemic. Similar to the global financial crisis (GFC), the spread of coronavirus (COVID-19) created a significant level of risk, causing investors to suffer losses in a very short period of time. We use a variety of methods, including nonstandard like mutual information and transfer entropy. The results that we obtained indicate that there are significant nonlinear correlations in the capital markets that can be practically applied for investment portfolio optimization. From an investor perspective, our findings suggest that in the wake of global crisis and pandemic outbreak, the benefits of diversification will be limited by the transfer of funds between developed and developing country markets. Our study provides an insight into the risk transfer theory in developed and emerging markets as well as a cutting-edge methodology designed for analyzing the connectedness of markets. We contribute to the studies which have examined the different stock markets’ response to different turbulences. The study confirms that specific market effects can still play a significant role because of the interconnection of different sectors of the global economy. Full article

(This article belongs to the Special Issue Entropy-Based Applications in Economics, Finance, and Management)

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18 pages, 2660 KiB

Open AccessArticle

Fuzzy Clustering Methods to Identify the Epidemiological Situation and Its Changes in European Countries during COVID-19

by Aleksandra Łuczak and Sławomir Kalinowski

Entropy 2022, 24(1), 14; https://doi.org/10.3390/e24010014 - 22 Dec 2021

Cited by 10 | Viewed by 4970

Abstract

The main research question concerned the identification of changes in the COVID-19 epidemiological situation using fuzzy clustering methods. This research used cross-sectional time series data obtained from the European Centre for Disease Prevention and Control. The identification of country types in terms of [...] Read more.

The main research question concerned the identification of changes in the COVID-19 epidemiological situation using fuzzy clustering methods. This research used cross-sectional time series data obtained from the European Centre for Disease Prevention and Control. The identification of country types in terms of epidemiological risk was carried out using the fuzzy c-means clustering method. We also used the entropy index to measure the degree of fuzziness in the classification and evaluate the uncertainty of epidemiological states. The proposed approach allowed us to identify countries’ epidemic states. Moreover, it also made it possible to determine the time of transition from one state to another, as well as to observe fluctuations during changes of state. Three COVID-19 epidemic states were identified in Europe, i.e., stabilisation, destabilisation, and expansion. The methodology is universal and can also be useful for other countries, as well as the research results being important for governments, politicians and other policy-makers working to mitigate the effects of the COVID-19 pandemic. Full article

(This article belongs to the Special Issue Entropy-Based Applications in Economics, Finance, and Management)

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12 pages, 258 KiB

Open AccessArticle

Using Entropy to Evaluate the Impact of Monetary Policy Shocks on Financial Networks

by Petre Caraiani and Alexandru Vasile Lazarec

Entropy 2021, 23(11), 1465; https://doi.org/10.3390/e23111465 - 06 Nov 2021

Cited by 3 | Viewed by 1547

Abstract

We analyze the changes in the financial network built using the Dow Jones Industrial Average components following monetary policy shocks. Monetary policy shocks are measured through unexpected changes in the federal funds rate in the United States. We determine the changes in the [...] Read more.

We analyze the changes in the financial network built using the Dow Jones Industrial Average components following monetary policy shocks. Monetary policy shocks are measured through unexpected changes in the federal funds rate in the United States. We determine the changes in the financial networks using singular value decomposition entropy and von Neumann entropy. The results indicate that unexpected positive shocks in monetary policy shocks lead to lower entropy. The results are robust to varying the window size used to construct financial networks, though they also depend on the type of entropy used. Full article

(This article belongs to the Special Issue Entropy-Based Applications in Economics, Finance, and Management)

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20 pages, 1175 KiB

Open AccessArticle

A Novel Extension of the Technique for Order Preference by Similarity to Ideal Solution Method with Objective Criteria Weights for Group Decision Making with Interval Numbers

by Dariusz Kacprzak

Entropy 2021, 23(11), 1460; https://doi.org/10.3390/e23111460 - 03 Nov 2021

Cited by 5 | Viewed by 1516

Abstract

This paper presents an extension of the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method with objective criteria weights for Group Decision Making (GDM) with Interval Numbers (INs). The proposed method is an alternative to popular and often used methods [...] Read more.

This paper presents an extension of the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method with objective criteria weights for Group Decision Making (GDM) with Interval Numbers (INs). The proposed method is an alternative to popular and often used methods that aggregate the decision matrices provided by the decision makers (DMs) into a single group matrix, which is the basis for determining objective criteria weights and ranking the alternatives. It does not use an aggregation operator, but a transformation of the decision matrices into criteria matrices, in the case of determining objective criteria weights, and into alternative matrices, in the case of the ranking of alternatives. This ensures that all the decision makers’ evaluations are taken into account instead of their certain average. The numerical example shows the ease of use of the proposed method, which can be implemented into common data analysis software such as Excel. Full article

(This article belongs to the Special Issue Entropy-Based Applications in Economics, Finance, and Management)

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17 pages, 1815 KiB

Open AccessArticle

Is Bitcoin Still a King? Relationships between Prices, Volatility and Liquidity of Cryptocurrencies during the Pandemic

by Barbara Będowska-Sójka, Agata Kliber and Aleksandra Rutkowska

Entropy 2021, 23(11), 1386; https://doi.org/10.3390/e23111386 - 22 Oct 2021

Cited by 7 | Viewed by 2258

Abstract

We try to establish the commonalities and leadership in the cryptocurrency markets by examining the mutual information and lead-lag relationships between Bitcoin and other cryptocurrencies from January 2019 to June 2021. We examine the transfer entropy between volatility and liquidity of seven highly [...] Read more.

We try to establish the commonalities and leadership in the cryptocurrency markets by examining the mutual information and lead-lag relationships between Bitcoin and other cryptocurrencies from January 2019 to June 2021. We examine the transfer entropy between volatility and liquidity of seven highly capitalized cryptocurrencies in order to determine the potential direction of information flow. We find that cryptocurrencies are strongly interrelated in returns and volatility but less in liquidity. We show that smaller and younger cryptocurrencies (such as Ripple’s XRP or Litecoin) have started to affect the returns of Bitcoin since the beginning of the pandemic. Regarding liquidity, the results of the dynamic time warping algorithm also suggest that the position of Monero has increased. Those outcomes suggest the gradual increase in the role of privacy-oriented cryptocurrencies. Full article

(This article belongs to the Special Issue Entropy-Based Applications in Economics, Finance, and Management)

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18 pages, 9260 KiB

Open AccessArticle

Coherence and Entropy of Credit Cycles across the Euro Area Candidate Countries

by Adina Criste, Iulia Lupu and Radu Lupu

Entropy 2021, 23(9), 1213; https://doi.org/10.3390/e23091213 - 14 Sep 2021

Cited by 2 | Viewed by 1615

Abstract

The pattern of financial cycles in the European Union has direct impacts on financial stability and economic sustainability in view of adoption of the euro. The purpose of the article is to identify the degree of coherence of credit cycles in the countries [...] Read more.

The pattern of financial cycles in the European Union has direct impacts on financial stability and economic sustainability in view of adoption of the euro. The purpose of the article is to identify the degree of coherence of credit cycles in the countries potentially seeking to adopt the euro with the credit cycle inside the Eurozone. We first estimate the credit cycles in the selected countries and in the euro area (at the aggregate level) and filter the series with the Hodrick–Prescott filter for the period 1999Q1–2020Q4. Based on these values, we compute the indicators that define the credit cycle similarity and synchronicity in the selected countries and a set of entropy measures (block entropy, entropy rate, Bayesian entropy) to show the high degree of heterogeneity, noting that the manifestation of the global financial crisis has changed the credit cycle patterns in some countries. Our novel approach provides analytical tools to cope with euro adoption decisions, showing how the coherence of credit cycles can be increased among European countries and how the national macroprudential policies can be better coordinated, especially in light of changes caused by the pandemic crisis. Full article

(This article belongs to the Special Issue Entropy-Based Applications in Economics, Finance, and Management)

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20 pages, 3368 KiB

Open AccessArticle

A Network Approach to the Study of the Dynamics of Risk Spillover in China’s Bond Market

by Zhewen Liao, Hongli Zhang, Kun Guo and Ning Wu

Entropy 2021, 23(7), 920; https://doi.org/10.3390/e23070920 - 20 Jul 2021

Cited by 9 | Viewed by 2949

Abstract

Since 2018, the bond market has surpassed the stock market, becoming the biggest investment area in China’s security market, and the systemic risks of China’s bond market are of non-negligible importance. Based on daily interest rate data of representative bond categories, this study [...] Read more.

Since 2018, the bond market has surpassed the stock market, becoming the biggest investment area in China’s security market, and the systemic risks of China’s bond market are of non-negligible importance. Based on daily interest rate data of representative bond categories, this study conducted a dynamic analysis based on generalized vector autoregressive volatility spillover variance decomposition, constructed a complex network, and adopted the minimum spanning tree method to clarify and analyze the risk propagation path between different bond types. It is found that the importance of each bond type is positively correlated with liquidity, transaction volume, and credit rating, and the inter-bank market is the most important market in the entire bond market, while interest rate bonds, bank bonds and urban investment bonds are important varieties with great systemic importance. In addition, the long-term trend of the dynamic spillover index of China’s bond market falls in line with the pace of the interest rate adjustments. To hold the bottom line of preventing financial systemic risks of China’s bond market, standard management, strict supervision, and timely regulation of the bond markets are required, and the structural entropy, as a useful indicator, also should be used in the risk management and monitoring. Full article

(This article belongs to the Special Issue Entropy-Based Applications in Economics, Finance, and Management)

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22 pages, 5362 KiB

Open AccessArticle

An Entropy-Based Approach to Measurement of Stock Market Depth

by Joanna Olbryś and Krzysztof Ostrowski

Entropy 2021, 23(5), 568; https://doi.org/10.3390/e23050568 - 03 May 2021

Cited by 7 | Viewed by 3749

Abstract

The aim of this study is to investigate market depth as a stock market liquidity dimension. A new methodology for market depth measurement exactly based on Shannon information entropy for high-frequency data is introduced and utilized. The proposed entropy-based market depth indicator is [...] Read more.

The aim of this study is to investigate market depth as a stock market liquidity dimension. A new methodology for market depth measurement exactly based on Shannon information entropy for high-frequency data is introduced and utilized. The proposed entropy-based market depth indicator is supported by an algorithm inferring the initiator of a trade. This new indicator seems to be a promising liquidity measure. Both market entropy and market liquidity can be directly measured by the new indicator. The findings of empirical experiments for real-data with a time stamp rounded to the nearest second from the Warsaw Stock Exchange (WSE) confirm that the new proxy enables us to effectively compare market depth and liquidity for different equities. Robustness tests and statistical analyses are conducted. Furthermore, an intra-day seasonality assessment is provided. Results indicate that the entropy-based approach can be considered as an auspicious market depth and liquidity proxy with an intuitive base for both theoretical and empirical analyses in financial markets. Full article

(This article belongs to the Special Issue Entropy-Based Applications in Economics, Finance, and Management)

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29 pages, 535 KiB

Open AccessEditor’s ChoiceArticle

Crowded Trades, Market Clustering, and Price Instability

by Marc van Kralingen, Diego Garlaschelli, Karolina Scholtus and Iman van Lelyveld

Entropy 2021, 23(3), 336; https://doi.org/10.3390/e23030336 - 12 Mar 2021

Cited by 3 | Viewed by 3771

Abstract

Crowded trades by similarly trading peers influence the dynamics of asset prices, possibly creating systemic risk. We propose a market clustering measure using granular trading data. For each stock, the clustering measure captures the degree of trading overlap among any two investors in [...] Read more.

Crowded trades by similarly trading peers influence the dynamics of asset prices, possibly creating systemic risk. We propose a market clustering measure using granular trading data. For each stock, the clustering measure captures the degree of trading overlap among any two investors in that stock, based on a comparison with the expected crowding in a null model where trades are maximally random while still respecting the empirical heterogeneity of both stocks and investors. We investigate the effect of crowded trades on stock price stability and present evidence that market clustering has a causal effect on the properties of the tails of the stock return distribution, particularly the positive tail, even after controlling for commonly considered risk drivers. Reduced investor pool diversity could thus negatively affect stock price stability. Full article

(This article belongs to the Special Issue Entropy-Based Applications in Economics, Finance, and Management)

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