Research

32 pages, 10388 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

The Cross-Sectional Intrinsic Entropy—A Comprehensive Stock Market Volatility Estimator

by Claudiu Vințe and Marcel Ausloos

Entropy 2022, 24(5), 623; https://doi.org/10.3390/e24050623 - 29 Apr 2022

Cited by 4 | Viewed by 2814

To take into account the temporal dimension of uncertainty in stock markets, this paper introduces a cross-sectional estimation of stock market volatility based on the intrinsic entropy model. The proposed cross-sectional intrinsic entropy (CSIE) is defined and computed as a daily [...] Read more.

To take into account the temporal dimension of uncertainty in stock markets, this paper introduces a cross-sectional estimation of stock market volatility based on the intrinsic entropy model. The proposed cross-sectional intrinsic entropy (CSIE) is defined and computed as a daily volatility estimate for the entire market, grounded on the daily traded prices—open, high, low, and close prices (OHLC)—along with the daily traded volume for all symbols listed on The New York Stock Exchange (NYSE) and The National Association of Securities Dealers Automated Quotations (NASDAQ). We perform a comparative analysis between the time series obtained from the CSIE and the historical volatility as provided by the estimators: close-to-close, Parkinson, Garman–Klass, Rogers–Satchell, Yang–Zhang, and intrinsic entropy (IE), defined and computed from historical OHLC daily prices of the Standard & Poor’s 500 index (S&P500), Dow Jones Industrial Average (DJIA), and the NASDAQ Composite index, respectively, for various time intervals. Our study uses an approximate 6000-day reference point, starting 1 January 2001, until 23 January 2022, for both the NYSE and the NASDAQ. We found that the CSIE market volatility estimator is consistently at least 10 times more sensitive to market changes, compared to the volatility estimate captured through the market indices. Furthermore, beta values confirm a consistently lower volatility risk for market indices overall, between 50% and 90% lower, compared to the volatility risk of the entire market in various time intervals and rolling windows. Full article

(This article belongs to the Special Issue Fractal and Multifractal Analysis of Complex Networks)

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18 pages, 976 KiB

Open AccessArticle

TLP-CCC: Temporal Link Prediction Based on Collective Community and Centrality Feature Fusion

by Yuhang Zhu, Shuxin Liu, Yingle Li and Haitao Li

Entropy 2022, 24(2), 296; https://doi.org/10.3390/e24020296 - 20 Feb 2022

Cited by 6 | Viewed by 1804

Abstract

In the domain of network science, the future link between nodes is a significant problem in social network analysis. Recently, temporal network link prediction has attracted many researchers due to its valuable real-world applications. However, the methods based on network structure similarity are [...] Read more.

In the domain of network science, the future link between nodes is a significant problem in social network analysis. Recently, temporal network link prediction has attracted many researchers due to its valuable real-world applications. However, the methods based on network structure similarity are generally limited to static networks, and the methods based on deep neural networks often have high computational costs. This paper fully mines the network structure information and time-domain attenuation information, and proposes a novel temporal link prediction method. Firstly, the network collective influence (CI) method is used to calculate the weights of nodes and edges. Then, the graph is divided into several community subgraphs by removing the weak link. Moreover, the biased random walk method is proposed, and the embedded representation vector is obtained by the modified Skip-gram model. Finally, this paper proposes a novel temporal link prediction method named TLP-CCC, which integrates collective influence, the community walk features, and the centrality features. Experimental results on nine real dynamic network data sets show that the proposed method performs better for area under curve (AUC) evaluation compared with the classical link prediction methods. Full article

(This article belongs to the Special Issue Fractal and Multifractal Analysis of Complex Networks)

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12 pages, 641 KiB

Open AccessArticle

Hypothetical Control of Fatal Quarrel Variability

by Bruce J. West

Entropy 2021, 23(12), 1693; https://doi.org/10.3390/e23121693 - 17 Dec 2021

Viewed by 1738

Abstract

Wars, terrorist attacks, as well as natural catastrophes typically result in a large number of casualties, whose distributions have been shown to belong to the class of Pareto’s inverse power laws (IPLs). The number of deaths resulting from terrorist attacks are herein fit [...] Read more.

Wars, terrorist attacks, as well as natural catastrophes typically result in a large number of casualties, whose distributions have been shown to belong to the class of Pareto’s inverse power laws (IPLs). The number of deaths resulting from terrorist attacks are herein fit by a double Pareto probability density function (PDF). We use the fractional probability calculus to frame our arguments and to parameterize a hypothetical control process to temper a Lévy process through a collective-induced potential. Thus, the PDF is shown to be a consequence of the complexity of the underlying social network. The analytic steady-state solution to the fractional Fokker-Planck equation (FFPE) is fit to a forty-year fatal quarrel (FQ) dataset. Full article

(This article belongs to the Special Issue Fractal and Multifractal Analysis of Complex Networks)

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18 pages, 2093 KiB

Open AccessArticle

Network Autoregressive Model for the Prediction of COVID-19 Considering the Disease Interaction in Neighboring Countries

by Arash Sioofy Khoojine, Mahdi Shadabfar, Vahid Reza Hosseini and Hadi Kordestani

Entropy 2021, 23(10), 1267; https://doi.org/10.3390/e23101267 - 28 Sep 2021

Cited by 12 | Viewed by 1836

Abstract

Predicting the way diseases spread in different societies has been thus far documented as one of the most important tools for control strategies and policy-making during a pandemic. This study is to propose a network autoregressive (NAR) model to forecast the number of [...] Read more.

Predicting the way diseases spread in different societies has been thus far documented as one of the most important tools for control strategies and policy-making during a pandemic. This study is to propose a network autoregressive (NAR) model to forecast the number of total currently infected cases with coronavirus disease 2019 (COVID-19) in Iran until the end of December 2021 in view of the disease interactions within the neighboring countries in the region. For this purpose, the COVID-19 data were initially collected for seven regional nations, including Iran, Turkey, Iraq, Azerbaijan, Armenia, Afghanistan, and Pakistan. Thenceforth, a network was established over these countries, and the correlation of the disease data was calculated. Upon introducing the main structure of the NAR model, a mathematical platform was subsequently provided to further incorporate the correlation matrix into the prediction process. In addition, the maximum likelihood estimation (MLE) was utilized to determine the model parameters and optimize the forecasting accuracy. Thereafter, the number of infected cases up to December 2021 in Iran was predicted by importing the correlation matrix into the NAR model formed to observe the impact of the disease interactions in the neighboring countries. In addition, the autoregressive integrated moving average (ARIMA) was used as a benchmark to compare and validate the NAR model outcomes. The results reveal that COVID-19 data in Iran have passed the fifth peak and continue on a downward trend to bring the number of total currently infected cases below 480,000 by the end of 2021. Additionally, 20%, 50%, 80% and 95% quantiles are provided along with the point estimation to model the uncertainty in the forecast. Full article

(This article belongs to the Special Issue Fractal and Multifractal Analysis of Complex Networks)

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17 pages, 6517 KiB

Open AccessArticle

Dynamic Time Warping Algorithm in Modeling Systemic Risk in the European Insurance Sector

by Anna Denkowska and Stanisław Wanat

Entropy 2021, 23(8), 1022; https://doi.org/10.3390/e23081022 - 08 Aug 2021

Cited by 7 | Viewed by 2092

Abstract

We are looking for tools to identify, model, and measure systemic risk in the insurance sector. To this aim, we investigated the possibilities of using the Dynamic Time Warping (DTW) algorithm in two ways. The first way of using DTW is to assess [...] Read more.

We are looking for tools to identify, model, and measure systemic risk in the insurance sector. To this aim, we investigated the possibilities of using the Dynamic Time Warping (DTW) algorithm in two ways. The first way of using DTW is to assess the suitability of the Minimum Spanning Trees’ (MST) topological indicators, which were constructed based on the tail dependence coefficients determined by the copula-DCC-GARCH model in order to establish the links between insurance companies in the context of potential shock contagion. The second way consists of using the DTW algorithm to group institutions by the similarity of their contribution to systemic risk, as expressed by DeltaCoVaR, in the periods distinguished. For the crises and the normal states identified during the period 2005–2019 in Europe, we analyzed the similarity of the time series of the topological indicators of MST, constructed for 38 European insurance institutions. The results obtained confirm the effectiveness of MST topological indicators for systemic risk identification and the evaluation of indirect links between insurance institutions. Full article

(This article belongs to the Special Issue Fractal and Multifractal Analysis of Complex Networks)

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19 pages, 4151 KiB

Open AccessEditor’s ChoiceArticle

Multifractal Behaviors of Stock Indices and Their Ability to Improve Forecasting in a Volatility Clustering Period

by Shuwen Zhang and Wen Fang

Entropy 2021, 23(8), 1018; https://doi.org/10.3390/e23081018 - 06 Aug 2021

Cited by 13 | Viewed by 2526

Abstract

The financial market is a complex system, which has become more complicated due to the sudden impact of the COVID-19 pandemic in 2020. As a result there may be much higher degree of uncertainty and volatility clustering in stock markets. How does this [...] Read more.

The financial market is a complex system, which has become more complicated due to the sudden impact of the COVID-19 pandemic in 2020. As a result there may be much higher degree of uncertainty and volatility clustering in stock markets. How does this “black swan” event affect the fractal behaviors of the stock market? How to improve the forecasting accuracy after that? Here we study the multifractal behaviors of 5-min time series of CSI300 and S&P500, which represents the two stock markets of China and United States. Using the Overlapped Sliding Window-based Multifractal Detrended Fluctuation Analysis (OSW-MF-DFA) method, we found that the two markets always have multifractal characteristics, and the degree of fractal intensified during the first panic period of pandemic. Based on the long and short-term memory which are described by fractal test results, we use the Gated Recurrent Unit (GRU) neural network model to forecast these indices. We found that during the large volatility clustering period, the prediction accuracy of the time series can be significantly improved by adding the time-varying Hurst index to the GRU neural network. Full article

(This article belongs to the Special Issue Fractal and Multifractal Analysis of Complex Networks)

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15 pages, 372 KiB

Open AccessArticle

Why Dilated Convolutional Neural Networks: A Proof of Their Optimality

by Jonatan Contreras, Martine Ceberio and Vladik Kreinovich

Entropy 2021, 23(6), 767; https://doi.org/10.3390/e23060767 - 18 Jun 2021

Cited by 1 | Viewed by 1691

Abstract

One of the most effective image processing techniques is the use of convolutional neural networks that use convolutional layers. In each such layer, the value of the layer’s output signal at each point is a combination of the layer’s input signals corresponding to [...] Read more.

One of the most effective image processing techniques is the use of convolutional neural networks that use convolutional layers. In each such layer, the value of the layer’s output signal at each point is a combination of the layer’s input signals corresponding to several neighboring points. To improve the accuracy, researchers have developed a version of this technique, in which only data from some of the neighboring points is processed. It turns out that the most efficient case—called dilated convolution—is when we select the neighboring points whose differences in both coordinates are divisible by some constant ℓ. In this paper, we explain this empirical efficiency by proving that for all reasonable optimality criteria, dilated convolution is indeed better than possible alternatives. Full article

(This article belongs to the Special Issue Fractal and Multifractal Analysis of Complex Networks)

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18 pages, 7262 KiB

Open AccessEditor’s ChoiceArticle

EEG Fractal Analysis Reflects Brain Impairment after Stroke

by Maria Rubega, Emanuela Formaggio, Franco Molteni, Eleonora Guanziroli, Roberto Di Marco, Claudio Baracchini, Mario Ermani, Nick S. Ward, Stefano Masiero and Alessandra Del Felice

Entropy 2021, 23(5), 592; https://doi.org/10.3390/e23050592 - 11 May 2021

Cited by 11 | Viewed by 3278

Abstract

Stroke is the commonest cause of disability. Novel treatments require an improved understanding of the underlying mechanisms of recovery. Fractal approaches have demonstrated that a single metric can describe the complexity of seemingly random fluctuations of physiological signals. We hypothesize that fractal algorithms [...] Read more.

Stroke is the commonest cause of disability. Novel treatments require an improved understanding of the underlying mechanisms of recovery. Fractal approaches have demonstrated that a single metric can describe the complexity of seemingly random fluctuations of physiological signals. We hypothesize that fractal algorithms applied to electroencephalographic (EEG) signals may track brain impairment after stroke. Sixteen stroke survivors were studied in the hyperacute (<48 h) and in the acute phase (∼1 week after stroke), and 35 stroke survivors during the early subacute phase (from 8 days to 32 days and after ∼2 months after stroke): We compared resting-state EEG fractal changes using fractal measures (i.e., Higuchi Index, Tortuosity) with 11 healthy controls. Both Higuchi index and Tortuosity values were significantly lower after a stroke throughout the acute and early subacute stage compared to healthy subjects, reflecting a brain activity which is significantly less complex. These indices may be promising metrics to track behavioral changes in the very early stage after stroke. Our findings might contribute to the neurorehabilitation quest in identifying reliable biomarkers for a better tailoring of rehabilitation pathways. Full article

(This article belongs to the Special Issue Fractal and Multifractal Analysis of Complex Networks)

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