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Orlando G, Lampart M. Expecting the Unexpected: Entropy and Multifractal Systems in Finance. ENTROPY (BASEL, SWITZERLAND) 2023; 25:1527. [PMID: 37998219 PMCID: PMC10670846 DOI: 10.3390/e25111527] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/01/2023] [Revised: 10/31/2023] [Accepted: 11/01/2023] [Indexed: 11/25/2023]
Abstract
Entropy serves as a measure of chaos in systems by representing the average rate of information loss about a phase point's position on the attractor. When dealing with a multifractal system, a single exponent cannot fully describe its dynamics, necessitating a continuous spectrum of exponents, known as the singularity spectrum. From an investor's point of view, a rise in entropy is a signal of abnormal and possibly negative returns. This means he has to expect the unexpected and prepare for it. To explore this, we analyse the New York Stock Exchange (NYSE) U.S. Index as well as its constituents. Through this examination, we assess their multifractal characteristics and identify market conditions (bearish/bullish markets) using entropy, an effective method for recognizing fluctuating fractal markets. Our findings challenge conventional beliefs by demonstrating that price declines lead to increased entropy, contrary to some studies in the literature that suggest that reduced entropy in market crises implies more determinism. Instead, we propose that bear markets are likely to exhibit higher entropy, indicating a greater chance of unexpected extreme events. Moreover, our study reveals a power-law behaviour and indicates the absence of variance.
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Affiliation(s)
- Giuseppe Orlando
- Department of Mathematics, University of Bari, Via Edoardo Orabona 4, 70125 Bari, Italy
- Department of Mathematics, University of Jaen, Campus Las Lagunillas s/n, 23071 Jaén, Spain
- Department of Economics, HSE University, 3A Kantemirovskaya Ulitsa, St. Petersburg 190121, Russia
| | - Marek Lampart
- IT4Innovations, VSB—Technical University of Ostrava, 17. Listopadu 2172/15, 708 00 Ostrava, Czech Republic;
- Department of Applied Mathematics, VSB—Technical University of Ostrava, 17. Listopadu 2172/15, 708 00 Ostrava, Czech Republic
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Guerrero J, Galiano MDC, Orlando G. Modeling COVID-19 pandemic with financial markets models: The case of Jaén (Spain). MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2023; 20:9080-9100. [PMID: 37161235 DOI: 10.3934/mbe.2023399] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/11/2023]
Abstract
The main objective of this work is to test whether some stochastic models typically used in financial markets could be applied to the COVID-19 pandemic. To this end, we have implemented the ARIMAX and Cox-Ingersoll-Ross (CIR) models originally designed for interest rate pricing but transformed by us into a forecasting tool. For the latter, which we denoted CIR*, both the Euler-Maruyama method and the Milstein method were used. Forecasts obtained with the maximum likelihood method have been validated with 95% confidence intervals and with statistical measures of goodness of fit, such as the root mean square error (RMSE). We demonstrate that the accuracy of the obtained results is consistent with the observations and sufficiently accurate to the point that the proposed CIR* framework could be considered a valid alternative to the classical ARIMAX for modelling pandemics.
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Affiliation(s)
- Julio Guerrero
- Department of Mathematics, University of Jaén, Campus de las Lagunillas s/n, Jaén 23071, Spain
| | | | - Giuseppe Orlando
- Department of Mathematics, University of Jaén, Campus de las Lagunillas s/n, Jaén 23071, Spain
- Department of Mathematics, University of Bari, via Edoardo Orabona 4, Bari 70125, Italy
- Department of Economics, HSE University, 16 Soyuza Pechatnikov Street, St Petersburg 190121, Russia
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Exploiting deterministic features in apparently stochastic data. Sci Rep 2022; 12:19843. [PMID: 36400910 PMCID: PMC9674651 DOI: 10.1038/s41598-022-23212-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/06/2022] [Accepted: 10/26/2022] [Indexed: 11/19/2022] Open
Abstract
Many processes in nature are the result of many coupled individual subsystems (like population dynamics or neurosystems). Not always such systems exhibit simple stable behaviors that in the past science has mostly focused on. Often, these systems are characterized by bursts of seemingly stochastic activity, interrupted by quieter periods. The hypothesis is that the presence of a strong deterministic ingredient is often obscured by the stochastic features. We test this by modeling classically stochastic considered real-world data from both, the stochastic as well as the deterministic approaches to find that the deterministic approach's results level with those from the stochastic side. Moreover, the deterministic approach is shown to reveal the full dynamical systems landscape, which can be exploited for steering the dynamics into a desired regime.
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Zimatore G, Cavagnaro M, Skarzynski PH, Hatzopoulos S. Detection of hearing losses (HL) via transient-evoked otoacoustic emissions: towards an automatic classification. Biomed Phys Eng Express 2022; 8. [PMID: 35724632 DOI: 10.1088/2057-1976/ac7a5e] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/26/2022] [Accepted: 06/20/2022] [Indexed: 11/11/2022]
Abstract
Transiently evoked otoacoustic emissions (TEOAEs) are routinely used in the hearing assessment of the auditory periphery. The major contribution of TEOAEs is the early detection of hearing losses in neonates, children, and adults. The evaluation of TEOAE responses by specific signal decomposition techniques offers numerous advantages for current and future research. One methodology, based on recurrence quantification analysis (RQA), can identify adult subjects presenting sensorineural hearing impairments. In two previous papers, the RQA-based approach was succesfully applied in identifying and classifying cases presenting noise and age related hearing losses. The current work investigates further two aspects of the previously proposed RQA-based analysis for hearing loss detection: (i) the reliability of a Training set built from different numbers of ears with normal hearing, and (ii) the threshold set of values of the key hearing loss detecting parameter RAD2D. Results: The Training set built from 158 healthy ears was found to be quite reliable and a similar but slightly minor performance was observed for the training set of 118 normal subjects, used in the past; the proposed ROC-curve method, optimizing the values of RAD2D, shows improved sensibility and specificity in one class discrimination. Conclusions: A complete and simplified procedure, based on the combined use of the traditional TEOAE reproducibility value and on values from the RQA-based RAD2D parameter, is proposed as an improved automatic classifier, in terms of sensitivity and specificity, for different types of hearing losses.
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Affiliation(s)
- Giovanna Zimatore
- Department of Theoretical and Applied Sciences Applied Physics, eCampus University, Via Isimbardi 10, Roma, Novedrate, 22060, ITALY
| | - Marta Cavagnaro
- Department of Information Engineering, Electronics and Telecommunications, University of Rome La Sapienza, via Eudossiana 18, Rome, Lazio, 00185, ITALY
| | - Piotr Henryk Skarzynski
- Department of Heart Failure and Cardiac Rehabilitation, Medical University of Warsaw, Żwirki i Wigury 61, Warszawa, Mazowieckie, 02-091, POLAND
| | - Stavros Hatzopoulos
- Clinic of Audiology & ENT, University of Ferrara, Via Aldo Moro 8, Ferrara, Ferrara, Emilia-Romagna, 44121, ITALY
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Unsupervised Clustering of Heartbeat Dynamics Allows for Real Time and Personalized Improvement in Cardiovascular Fitness. SENSORS 2022; 22:s22113974. [PMID: 35684596 PMCID: PMC9182749 DOI: 10.3390/s22113974] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/22/2022] [Revised: 05/11/2022] [Accepted: 05/20/2022] [Indexed: 02/06/2023]
Abstract
VO2max index has a significant impact on overall health. Its estimation through wearables notifies the user of his level of fitness but cannot provide a detailed analysis of the time intervals in which heartbeat dynamics are changed and/or fatigue is emerging. Here, we developed a multiple modality biosignal processing method to investigate running sessions to characterize in real time heartbeat dynamics in response to external energy demand. We isolated dynamic regimes whose fraction increases with the VO2max and with the emergence of neuromuscular fatigue. This analysis can be extremely valuable by providing personalized feedback about the user’s fitness level improvement that can be realized by developing personalized exercise plans aimed to target a contextual increase in the dynamic regime fraction related to VO2max increase, at the expense of the dynamic regime fraction related to the emergence of fatigue. These strategies can ultimately result in the reduction in cardiovascular risk.
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Mastroeni L, Vellucci P. Replication in Energy Markets: Use and Misuse of Chaos Tools. ENTROPY 2022; 24:e24050701. [PMID: 35626584 PMCID: PMC9141531 DOI: 10.3390/e24050701] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/16/2022] [Revised: 05/10/2022] [Accepted: 05/14/2022] [Indexed: 12/02/2022]
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 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.
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Active management strategy for supply chain system using nonlinear control synthesis. INTERNATIONAL JOURNAL OF DYNAMICS AND CONTROL 2022; 10:1981-1995. [PMID: 35310521 PMCID: PMC8916510 DOI: 10.1007/s40435-021-00901-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/20/2021] [Revised: 11/05/2021] [Accepted: 11/19/2021] [Indexed: 11/16/2022]
Abstract
Nonlinear dynamical behaviours with chaotic phenomena are commonly observed in a typical logistics model and supply chain system. Bullwhip effect has been widely recognized as one of the main issues on affecting the supply chain management. In essence, this phenomenon will lead to unnecessary consumption and waste of natural and social resources by demand variability amplification as moving up in the supply chain networks. However, traditional modelling approaches may become complicated in dealing with uncertainty and chaotic behaviour that are prevalent in real supply chains. System dynamics theory has been employed as a potentially effective strategy to cope with chaotic supply chains which are unpredictable behaviours in time. Four-dimensional differential equations which exhibit chaotic behaviours are constructed to describe a multi-echelon supply chain with bullwhip effect. Furthermore, modern control theory is applied to deal with the multi-stage supply chain optimization problems against disruptions. Specifically, the novel fractional order adaptive sliding mode control (FO-ASMC) algorithm has been implemented for ensuring efficient supply chain management. In addition, the chaos synchronization scheme is implemented in an attempt to regulate the supply chain systems under the impact of extensive uncertainties caused by tumultuous real market. It is found that the chaos synchronization is effectively realised by new FO-ASMC theory to manage advanced supply chain networks. Finally, this advanced management optimization offers a new class of intelligent applications that connects demand to supply and planning to execution across the entire supply chains.
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Financial markets' deterministic aspects modeled by a low-dimensional equation. Sci Rep 2022; 12:1693. [PMID: 35105929 PMCID: PMC8807815 DOI: 10.1038/s41598-022-05765-z] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2021] [Accepted: 01/18/2022] [Indexed: 11/08/2022] Open
Abstract
We ask whether empirical finance market data (Financial Stress Index, swap and equity, emerging and developed, corporate and government, short and long maturity), with their recently observed alternations between calm periods and financial turmoil, could be described by a low-dimensional deterministic model, or whether this requests a stochastic approach. We find that a deterministic model performs at least as well as one of the best stochastic models, but may offer additional insight into the essential mechanisms that drive financial markets.
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Lampart M, Lampartová A, Orlando G. On extensive dynamics of a Cournot heterogeneous model with optimal response. CHAOS (WOODBURY, N.Y.) 2022; 32:023124. [PMID: 35232032 DOI: 10.1063/5.0082439] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/15/2021] [Accepted: 01/31/2022] [Indexed: 06/14/2023]
Abstract
The objective of this paper is the study of the dynamical properties analysis of an original specification of the classical Cournot heterogeneous model with optimal response; specifically, a new approach that considers ordinal utility instead of cardinal monetary amounts is proposed where the classical decision of quantity is disentangled from the decision on imitation. The analysis is performed by means of bifurcation diagrams, the 0-1 test for chaos, power spectral density, histograms, and trajectory analysis. For this purpose, a new perturbation parameter ε of the initial condition is introduced, and together with the intensity of choice parameter β determining the share of responders vs imitators, the system is researched. Depending on ε and β, extreme reach dynamics, and coexisting attractors, periodic and chaotic trajectories are investigated through massive simulations. Those dynamics represent alternation between stability, cycles and chaos in the market. As the dynamics are completely endogenous, it means that swings in economy are intrinsic to the system and that they may persist unless controlled.
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Affiliation(s)
- Marek Lampart
- IT4Innovations, VSB-Technical University of Ostrava, 17. listopadu 2172/15, 708 00 Ostrava, Czech Republic
| | - Alžběta Lampartová
- IT4Innovations, VSB-Technical University of Ostrava, 17. listopadu 2172/15, 708 00 Ostrava, Czech Republic
| | - Giuseppe Orlando
- Department of Economics and Finance, University of Bari, Via C. Rosalba 53, Bari 70125, Italy
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Zimatore G, Falcioni L, Gallotta MC, Bonavolontà V, Campanella M, De Spirito M, Guidetti L, Baldari C. Recurrence quantification analysis of heart rate variability to detect both ventilatory thresholds. PLoS One 2021; 16:e0249504. [PMID: 34618821 PMCID: PMC8496840 DOI: 10.1371/journal.pone.0249504] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2021] [Accepted: 09/23/2021] [Indexed: 12/01/2022] Open
Abstract
Aims of this study were: to verify if Recurrence Quantification Analysis (RQA) of Heart Rate Variability (HRV) time series could determine both ventilatory thresholds in individuals with different fitness levels, and to assess the validity of RQA method compared to gas-exchange method (GE). The two thresholds were estimated in thirty young individuals during incremental exercise on cycle-ergometer: Heart rate (HR), Oxygen consumption (VO2) and Workload were measured by the two methods (RQA and GE). Repeated measures ANOVA was used to assess main effects of methods and methods-by-groups interaction effects for HR, VO2 and Workload at aerobic (AerT) and anaerobic (AnT) thresholds. Validity of RQA at both thresholds was assessed for HR, VO2 and Workload by Ordinary Least Products (OLP) regression, Typical Percentage Error (TE), Intraclass Correlation Coefficients (ICC) and the Bland Altman plots. No methods-by-groups interaction effects were detected for HR, VO2 and Workload at AerT and AnT. The OLP analysis showed that at both thresholds RQA and GE methods had very strong correlations (r >0.8) in all variables (HR, VO2 and Workload). Slope and intercept values always included the 1 and the 0, respectively. At AerT the TE ranged from 4.02% (5.48 bpm) to 10.47% (8.53 Watts) (HR and Workload, respectively) and in all variables ICC values were excellent (≥0.85). At AnT the TE ranged from 2.53% (3.98 bpm) to 6.64% (7.81 Watts) (HR and Workload, respectively) and in all variables ICC values were excellent (≥0.90). Therefore, RQA of HRV time series is a new valid approach to determine both ventilatory thresholds in individuals with different physical fitness levels, it can be used when gas analysis is not possible or not convenient.
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Affiliation(s)
- Giovanna Zimatore
- Department of Theoretical and Applied Sciences, eCampus University, Novedrate (CO), Italy
- IMM-CNR, Bologna, Italy
- * E-mail: ,
| | - Lavinia Falcioni
- Department of Movement, Human and Health Sciences, University of Rome “Foro Italico”, Rome, Italy
| | - Maria Chiara Gallotta
- Department of Physiology and Pharmacology "Vittorio Erspamer", Sapienza University of Rome, Rome, Italy
| | - Valerio Bonavolontà
- Department of Basic Medical Sciences, Neuroscience and Sense Organs, University “Aldo Moro”, Bari, Italy
| | - Matteo Campanella
- Department of Theoretical and Applied Sciences, eCampus University, Novedrate (CO), Italy
| | - Marco De Spirito
- Fondazione Policlinico Universitario A. Gemelli IRCCS, Università Cattolica del Sacro Cuore Rome, Rome, Italy
| | | | - Carlo Baldari
- Department of Theoretical and Applied Sciences, eCampus University, Novedrate (CO), Italy
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