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Spasojević D, Marinković M, Jovković D, Janićević S, Laurson L, Djordjević A. Barkhausen noise in disordered striplike ferromagnets: Experiment versus simulations. Phys Rev E 2024; 109:024110. [PMID: 38491707 DOI: 10.1103/physreve.109.024110] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2023] [Accepted: 01/29/2024] [Indexed: 03/18/2024]
Abstract
In this work, we present a systematic comparison of the results obtained from the low-frequency Barkhausen noise recordings in nanocrystalline samples with those from the numerical simulations of the random-field Ising model systems. We performed measurements at room temperature on a field-driven metallic glass stripe made of VITROPERM 800 R, a nanocrystalline iron-based material with an excellent combination of soft and magnetic properties, making it a cutting-edge material for a wide range of applications. Given that the Barkhausen noise emissions emerging along a hysteresis curve are stochastic and depend in general on a variety of factors (such as distribution of disorder due to impurities or defects, varied size of crystal grains, type of domain structure, driving rate of the external magnetic field, sample shape and temperature, etc.), adequate theoretical modeling is essential for their interpretation and prediction. Here the Random field Ising model, specifically its athermal nonequilibrium version with the finite driving rate, stands out as an appropriate choice due to the material's nanocrystalline structure and high Curie temperature. We performed a systematic analysis of the signal properties and magnetization avalanches comparing the outcomes of the numerical model and experiments carried out in a two-decade-wide range of the external magnetic field driving rates. Our results reveal that with a suitable choice of parameters, a considerable match with the experimental results is achieved, indicating that this model can accurately describe the Barkhausen noise features in nanocrystalline samples.
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Affiliation(s)
- Djordje Spasojević
- Faculty of Physics, University of Belgrade, P. O. Box 44, 11001 Belgrade, Republic of Serbia
| | - Miloš Marinković
- Faculty of Physics, University of Belgrade, P. O. Box 44, 11001 Belgrade, Republic of Serbia
| | - Dragutin Jovković
- Faculty of Mining and Geology, University of Belgrade, P. O. Box 162, 11000 Belgrade, Republic of Serbia
| | - Sanja Janićević
- Faculty of Science, University of Kragujevac, P. O. Box 60, 34000 Kragujevac, Republic of Serbia
| | - Lasse Laurson
- Computational Physics Laboratory, Tampere University, P. O. Box 692, FI-33014 Tampere, Finland
| | - Antonije Djordjević
- School of Electrical Engineering, University of Belgrade, 11000 Belgrade, Republic of Serbia and Serbian Academy of Sciences and Arts, 11000 Belgrade, Republic of Serbia
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Multifractal Company Market: An Application to the Stock Market Indices. ENTROPY 2022; 24:e24010130. [PMID: 35052156 PMCID: PMC8774673 DOI: 10.3390/e24010130] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/30/2021] [Revised: 01/12/2022] [Accepted: 01/12/2022] [Indexed: 11/16/2022]
Abstract
Using the multiscale normalized partition function, we exploit the multifractal analysis based on directly measurable shares of companies in the market. We present evidence that markets of competing firms are multifractal/multiscale. We verified this by (i) using our model that described the critical properties of the company market and (ii) analyzing a real company market defined by the S&P500 index. As the valuable reference case, we considered a four-group market model that skillfully reconstructs this index’s empirical data. We point out that a four-group company market organization is universal because it can perfectly describe the essential features of the spectrum of dimensions, regardless of the analyzed series of shares. The apparent differences from the empirical data appear only at the level of subtle effects.
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Klamut J, Kutner R, Gubiec T, Struzik ZR. Multibranch multifractality and the phase transitions in time series of mean interevent times. Phys Rev E 2020; 101:063303. [PMID: 32688462 DOI: 10.1103/physreve.101.063303] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/10/2018] [Accepted: 04/30/2020] [Indexed: 11/07/2022]
Abstract
Empirical time series of interevent or waiting times are investigated using a modified Multifractal Detrended Fluctuation Analysis operating on fluctuations of mean detrended dynamics. The core of the extended multifractal analysis is the nonmonotonic behavior of the generalized Hurst exponent h(q)-the fundamental exponent in the study of multifractals. The consequence of this behavior is the nonmonotonic behavior of the coarse Hölder exponent α(q) leading to multibranchedness of the spectrum of dimensions. The Legendre-Fenchel transform is used instead of the routinely used canonical Legendre (single-branched) contact transform. Thermodynamic consequences of the multibranched multifractality are revealed. These are directly expressed in the language of phase transitions between thermally stable, metastable, and unstable phases. These phase transitions are of the first and second orders according to Mandelbrot's modified Ehrenfest classification. The discovery of multibranchedness is tantamount in significance to extending multifractal analysis.
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Affiliation(s)
- Jarosław Klamut
- Faculty of Physics, University of Warsaw, Pasteur Street 5, PL-02093 Warsaw, Poland
| | | | - Tomasz Gubiec
- Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215, USA and Faculty of Physics, University of Warsaw, Pasteur Street 5, PL-02093 Warsaw, Poland
| | - Zbigniew R Struzik
- University of Tokyo, Bunkyo-ku, Tokyo 113-8655, Japan and Advanced Center for Computing and Communication, RIKEN, 2-1 Hirosawa, Wako 351-0198, Saitama, Japan
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Jiang ZQ, Xie WJ, Zhou WX, Sornette D. Multifractal analysis of financial markets: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2019; 82:125901. [PMID: 31505468 DOI: 10.1088/1361-6633/ab42fb] [Citation(s) in RCA: 45] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Multifractality is ubiquitously observed in complex natural and socioeconomic systems. Multifractal analysis provides powerful tools to understand the complex nonlinear nature of time series in diverse fields. Inspired by its striking analogy with hydrodynamic turbulence, from which the idea of multifractality originated, multifractal analysis of financial markets has bloomed, forming one of the main directions of econophysics. We review the multifractal analysis methods and multifractal models adopted in or invented for financial time series and their subtle properties, which are applicable to time series in other disciplines. We survey the cumulating evidence for the presence of multifractality in financial time series in different markets and at different time periods and discuss the sources of multifractality. The usefulness of multifractal analysis in quantifying market inefficiency, in supporting risk management and in developing other applications is presented. We finally discuss open problems and further directions of multifractal analysis.
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Affiliation(s)
- Zhi-Qiang Jiang
- Research Center for Econophysics, East China University of Science and Technology, Shanghai 200237, People's Republic of China. Department of Finance, School of Business, East China University of Science and Technology, Shanghai 200237, People's Republic of China
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Lima GZDS, Corso G, Correa MA, Sommer RL, Ivanov PC, Bohn F. Universal temporal characteristics and vanishing of multifractality in Barkhausen avalanches. Phys Rev E 2017; 96:022159. [PMID: 28950597 DOI: 10.1103/physreve.96.022159] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2017] [Indexed: 06/07/2023]
Abstract
Barkhausen effect in ferromagnetic materials provides an excellent area for investigating scaling phenomena found in disordered systems exhibiting crackling noise. The critical dynamics is characterized by random pulses or avalanches with scale-invariant properties, power-law distributions, and universal features. However, the traditional Barkhausen avalanches statistics may not be sufficient to fully characterize the complex temporal correlation of the magnetic domain walls dynamics. Here we focus on the multifractal scenario to quantify the temporal scaling characteristics of Barkhausen avalanches in polycrystalline and amorphous ferromagnetic films with thicknesses from 50 to 1000 nm. We show that the multifractal properties are dependent on film thickness, although they seem to be insensitive to the structural character of the materials. Moreover, we observe for the first time the vanishing of the multifractality in the domain walls dynamics. As the thickness is reduced, the multifractal behavior gives place to a monofractal one over the entire range of time scales. This reorganization in the temporal scaling characteristics of Barkhausen avalanches is understood as a universal restructuring associated to the dimensional crossover, from three- to two-dimensional magnetization dynamics.
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Affiliation(s)
- G Z Dos Santos Lima
- Escola de Ciências e Tecnologia, Universidade Federal do Rio Grande do Norte, 59078-970 Natal, RN, Brazil
- Departamento de Biofísica e Farmacologia, Universidade Federal do Rio Grande do Norte, 59078-970 Natal, RN, Brazil
- Keck Laboratory for Network Physiology, Department of Physics, Boston University, Boston, Massachusetts 02215, USA
| | - G Corso
- Departamento de Biofísica e Farmacologia, Universidade Federal do Rio Grande do Norte, 59078-970 Natal, RN, Brazil
| | - M A Correa
- Departamento de Física, Universidade Federal do Rio Grande do Norte, 59078-900 Natal, RN, Brazil
| | - R L Sommer
- Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150, Urca, 22290-180 Rio de Janeiro, RJ, Brazil
| | - P Ch Ivanov
- Keck Laboratory for Network Physiology, Department of Physics, Boston University, Boston, Massachusetts 02215, USA
- Harvard Medical School and Division of Sleep Medicine, Brigham and Women Hospital, Boston, Massachusetts 02115, USA
- Institute of Solid State Physics, Bulgarian Academy of Sciences, Sofia 1784, Bulgaria
| | - F Bohn
- Departamento de Física, Universidade Federal do Rio Grande do Norte, 59078-900 Natal, RN, Brazil
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Denys M, Gubiec T, Kutner R, Jagielski M, Stanley HE. Universality of market superstatistics. Phys Rev E 2016; 94:042305. [PMID: 27841535 DOI: 10.1103/physreve.94.042305] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2015] [Indexed: 11/07/2022]
Abstract
We use a key concept of the continuous-time random walk formalism, i.e., continuous and fluctuating interevent times in which mutual dependence is taken into account, to model market fluctuation data when traders experience excessive (or superthreshold) losses or excessive (or superthreshold) profits. We analytically derive a class of "superstatistics" that accurately model empirical market activity data supplied by Bogachev, Ludescher, Tsallis, and Bunde that exhibit transition thresholds. We measure the interevent times between excessive losses and excessive profits and use the mean interevent discrete (or step) time as a control variable to derive a universal description of empirical data collapse. Our dominant superstatistic value is a power-law corrected by the lower incomplete gamma function, which asymptotically tends toward robustness but initially gives an exponential. We find that the scaling shape exponent that drives our superstatistics subordinates itself and a "superscaling" configuration emerges. Thanks to the Weibull copula function, our approach reproduces the empirically proven dependence between successive interevent times. We also use the approach to calculate a dynamic risk function and hence the dynamic VaR, which is significant in financial risk analysis. Our results indicate that there is a functional (but not literal) balance between excessive profits and excessive losses that can be described using the same body of superstatistics but different calibration values and driving parameters. We also extend our original approach to cover empirical seismic activity data (e.g., given by Corral), the interevent times of which range from minutes to years. Superpositioned superstatistics is another class of superstatistics that protects power-law behavior both for short- and long-time behaviors. These behaviors describe well the collapse of seismic activity data and capture so-called volatility clustering phenomena.
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Affiliation(s)
- Mateusz Denys
- Faculty of Physics, University of Warsaw, Pasteur 5, PL-02093 Warsaw, Poland
| | - Tomasz Gubiec
- Faculty of Physics, University of Warsaw, Pasteur 5, PL-02093 Warsaw, Poland
| | - Ryszard Kutner
- Faculty of Physics, University of Warsaw, Pasteur 5, PL-02093 Warsaw, Poland
| | - Maciej Jagielski
- Department of Management, Technology and Economics, ETHZ, Scheuchzerstrasse 7, CH-8092 Zürich, Switzerland; Faculty of Physics, University of Warsaw, Pasteur 5, PL-02093 Warsaw, Poland; and Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215, USA
| | - H Eugene Stanley
- Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215, USA
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Kwapień J, Oświęcimka P, Drożdż S. Detrended fluctuation analysis made flexible to detect range of cross-correlated fluctuations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:052815. [PMID: 26651752 DOI: 10.1103/physreve.92.052815] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/01/2015] [Indexed: 06/05/2023]
Abstract
The detrended cross-correlation coefficient ρ(DCCA) has recently been proposed to quantify the strength of cross-correlations on different temporal scales in bivariate, nonstationary time series. It is based on the detrended cross-correlation and detrended fluctuation analyses (DCCA and DFA, respectively) and can be viewed as an analog of the Pearson coefficient in the case of the fluctuation analysis. The coefficient ρ(DCCA) works well in many practical situations but by construction its applicability is limited to detection of whether two signals are generally cross-correlated, without the possibility to obtain information on the amplitude of fluctuations that are responsible for those cross-correlations. In order to introduce some related flexibility, here we propose an extension of ρ(DCCA) that exploits the multifractal versions of DFA and DCCA: multifractal detrended fluctuation analysis and multifractal detrended cross-correlation analysis, respectively. The resulting new coefficient ρ(q) not only is able to quantify the strength of correlations but also allows one to identify the range of detrended fluctuation amplitudes that are correlated in two signals under study. We show how the coefficient ρ(q) works in practical situations by applying it to stochastic time series representing processes with long memory: autoregressive and multiplicative ones. Such processes are often used to model signals recorded from complex systems and complex physical phenomena like turbulence, so we are convinced that this new measure can successfully be applied in time-series analysis. In particular, we present an example of such application to highly complex empirical data from financial markets. The present formulation can straightforwardly be extended to multivariate data in terms of the q-dependent counterpart of the correlation matrices and then to the network representation.
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Affiliation(s)
- Jarosław Kwapień
- Institute of Nuclear Physics, Polish Academy of Sciences, Kraków, Poland
| | - Paweł Oświęcimka
- Institute of Nuclear Physics, Polish Academy of Sciences, Kraków, Poland
| | - Stanisław Drożdż
- Institute of Nuclear Physics, Polish Academy of Sciences, Kraków, Poland
- Faculty of Physics, Mathematics and Computer Science, Cracow University of Technology, Kraków, Poland
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Ross GJ, Jones T. Understanding the heavy-tailed dynamics in human behavior. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:062809. [PMID: 26172756 DOI: 10.1103/physreve.91.062809] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/24/2014] [Indexed: 06/04/2023]
Abstract
The recent availability of electronic data sets containing large volumes of communication data has made it possible to study human behavior on a larger scale than ever before. From this, it has been discovered that across a diverse range of data sets, the interevent times between consecutive communication events obey heavy-tailed power law dynamics. Explaining this has proved controversial, and two distinct hypotheses have emerged. The first holds that these power laws are fundamental, and arise from the mechanisms such as priority queuing that humans use to schedule tasks. The second holds that they are statistical artifacts which only occur in aggregated data when features such as circadian rhythms and burstiness are ignored. We use a large social media data set to test these hypotheses, and find that although models that incorporate circadian rhythms and burstiness do explain part of the observed heavy tails, there is residual unexplained heavy-tail behavior which suggests a more fundamental cause. Based on this, we develop a quantitative model of human behavior which improves on existing approaches and gives insight into the mechanisms underlying human interactions.
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Affiliation(s)
- Gordon J Ross
- Department of Statistical Science/IRDR, University College London, Gower Street, London WC1E 6BT, United Kingdom
| | - Tim Jones
- Department of Computer Science, University of Bristol, Woodland Road, Bristol BS8 1UB, United Kingdom
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9
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Budroni MA, Pilosu V, Delogu F, Rustici M. Multifractal properties of ball milling dynamics. CHAOS (WOODBURY, N.Y.) 2014; 24:023117. [PMID: 24985431 DOI: 10.1063/1.4875259] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
This work focuses on the dynamics of a ball inside the reactor of a ball mill. We show that the distribution of collisions at the reactor walls exhibits multifractal properties in a wide region of the parameter space defining the geometrical characteristics of the reactor and the collision elasticity. This feature points to the presence of restricted self-organized zones of the reactor walls where the ball preferentially collides and the mechanical energy is mainly dissipated.
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Affiliation(s)
- M A Budroni
- Dipartimento di Chimica e Farmacia, Università degli Studi di Sassari, Via Vienna 2, Sassari 07100, Italy
| | - V Pilosu
- Dipartimento di Chimica e Farmacia, Università degli Studi di Sassari, Via Vienna 2, Sassari 07100, Italy
| | - F Delogu
- Dipartimento di Ingegneria Meccanica, Chimica, e dei Materiali, Università degli Studi di Cagliari, via Marengo 2, Cagliari 09123, Italy
| | - M Rustici
- Dipartimento di Chimica e Farmacia, Università degli Studi di Sassari, Via Vienna 2, Sassari 07100, Italy
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Ivanov PC, Yuen A, Perakakis P. Impact of stock market structure on intertrade time and price dynamics. PLoS One 2014; 9:e92885. [PMID: 24699376 PMCID: PMC3974723 DOI: 10.1371/journal.pone.0092885] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/03/2013] [Accepted: 02/27/2014] [Indexed: 11/19/2022] Open
Abstract
We analyse times between consecutive transactions for a diverse group of stocks registered on the NYSE and NASDAQ markets, and we relate the dynamical properties of the intertrade times with those of the corresponding price fluctuations. We report that market structure strongly impacts the scale-invariant temporal organisation in the transaction timing of stocks, which we have observed to have long-range power-law correlations. Specifically, we find that, compared to NYSE stocks, stocks registered on the NASDAQ exhibit significantly stronger correlations in their transaction timing on scales within a trading day. Further, we find that companies that transfer from the NASDAQ to the NYSE show a reduction in the correlation strength of transaction timing on scales within a trading day, indicating influences of market structure. We also report a persistent decrease in correlation strength of intertrade times with increasing average intertrade time and with corresponding decrease in companies' market capitalization–a trend which is less pronounced for NASDAQ stocks. Surprisingly, we observe that stronger power-law correlations in intertrade times are coupled with stronger power-law correlations in absolute price returns and higher price volatility, suggesting a strong link between the dynamical properties of intertrade times and the corresponding price fluctuations over a broad range of time scales. Comparing the NYSE and NASDAQ markets, we demonstrate that the stronger correlations we find in intertrade times for NASDAQ stocks are associated with stronger correlations in absolute price returns and with higher volatility, suggesting that market structure may affect price behavior through information contained in transaction timing. These findings do not support the hypothesis of universal scaling behavior in stock dynamics that is independent of company characteristics and stock market structure. Further, our results have implications for utilising transaction timing patterns in price prediction and risk management optimization on different stock markets.
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Affiliation(s)
- Plamen Ch. Ivanov
- Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts, United States of America
- Harvard Medical School and Division of Sleep Medicine, Brigham and Women's Hospital, Boston, Massachusetts, United States of America
- Institute of Solid State Physics, Bulgarian Academy of Sciences, Sofia, Bulgaria
- * E-mail:
| | - Ainslie Yuen
- Signal Processing Laboratory, Department of Engineering, Cambridge University, Cambridge, United Kingdom
| | - Pandelis Perakakis
- Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts, United States of America
- Laboratory of Experimental Economics, University Jaume I, Castellón, Spain
- Mind, Brain and Behaviour Research Centre (CIMCYC), University of Granada, Granada, Spain
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Oświecimka P, Drożdż S, Forczek M, Jadach S, Kwapień J. Detrended cross-correlation analysis consistently extended to multifractality. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:023305. [PMID: 25353603 DOI: 10.1103/physreve.89.023305] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/28/2013] [Indexed: 06/04/2023]
Abstract
We propose an algorithm, multifractal cross-correlation analysis (MFCCA), which constitutes a consistent extension of the detrended cross-correlation analysis and is able to properly identify and quantify subtle characteristics of multifractal cross-correlations between two time series. Our motivation for introducing this algorithm is that the already existing methods, like multifractal extension, have at best serious limitations for most of the signals describing complex natural processes and often indicate multifractal cross-correlations when there are none. The principal component of the present extension is proper incorporation of the sign of fluctuations to their generalized moments. Furthermore, we present a broad analysis of the model fractal stochastic processes as well as of the real-world signals and show that MFCCA is a robust and selective tool at the same time and therefore allows for a reliable quantification of the cross-correlative structure of analyzed processes. In particular, it allows one to identify the boundaries of the multifractal scaling and to analyze a relation between the generalized Hurst exponent and the multifractal scaling parameter λ(q). This relation provides information about the character of potential multifractality in cross-correlations and thus enables a deeper insight into dynamics of the analyzed processes than allowed by any other related method available so far. By using examples of time series from the stock market, we show that financial fluctuations typically cross-correlate multifractally only for relatively large fluctuations, whereas small fluctuations remain mutually independent even at maximum of such cross-correlations. Finally, we indicate possible utility of MFCCA to study effects of the time-lagged cross-correlations.
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Affiliation(s)
- Paweł Oświecimka
- Institute of Nuclear Physics, Polish Academy of Sciences, PL 31-342 Kraków, Poland
| | - Stanisław Drożdż
- Institute of Nuclear Physics, Polish Academy of Sciences, PL 31-342 Kraków, Poland and Faculty of Physics, Mathematics and Computer Science, Cracow University of Technology, PL 31-155 Kraków, Poland
| | - Marcin Forczek
- Institute of Nuclear Physics, Polish Academy of Sciences, PL 31-342 Kraków, Poland
| | - Stanisław Jadach
- Institute of Nuclear Physics, Polish Academy of Sciences, PL 31-342 Kraków, Poland
| | - Jarosław Kwapień
- Institute of Nuclear Physics, Polish Academy of Sciences, PL 31-342 Kraków, Poland
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Dos Santos Lima GZ, Corrêa MA, Sommer RL, Bohn F. Multifractality in domain wall dynamics of a ferromagnetic film. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:066117. [PMID: 23368014 DOI: 10.1103/physreve.86.066117] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/15/2012] [Indexed: 06/01/2023]
Abstract
We investigate the multifractal properties in the dynamics of domain walls of a ferromagnetic film. We apply the Multifractal Detrended Fluctuation Analysis method in experimental Barkhausen noise time series measured in a 1000-nm-thick Permalloy film under different driving magnetic field frequencies, and calculate the fluctuation function F_{q}(s), generalized Hurst exponent h(q), multifractal scaling exponent τ(q), and the multifractal spectrum f(α). Based on this procedure, we provide experimental evidence of multifractality in the dynamics of domain walls in ferromagnetic films and identify a rich and strong multifractal behavior, revealed by the changes of the scaling properties of over the entire Barkhausen noise signal, independently of the driving magnetic field rate employed in the experiment.
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Affiliation(s)
- G Z Dos Santos Lima
- Escola de Ciências e Tecnologia, Universidade Federal do Rio Grande do Norte, 59078-970 Natal, RN, Brazil.
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Filimonov V, Sornette D. Quantifying reflexivity in financial markets: toward a prediction of flash crashes. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:056108. [PMID: 23004822 DOI: 10.1103/physreve.85.056108] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/26/2012] [Revised: 04/02/2012] [Indexed: 06/01/2023]
Abstract
We introduce a measure of activity of financial markets that provides a direct access to their level of endogeneity. This measure quantifies how much of price changes is due to endogenous feedback processes, as opposed to exogenous news. For this, we calibrate the self-excited conditional Poisson Hawkes model, which combines in a natural and parsimonious way exogenous influences with self-excited dynamics, to the E-mini S&P 500 futures contracts traded in the Chicago Mercantile Exchange from 1998 to 2010. We find that the level of endogeneity has increased significantly from 1998 to 2010, with only 70% in 1998 to less than 30% since 2007 of the price changes resulting from some revealed exogenous information. Analogous to nuclear plant safety measures concerned with avoiding "criticality," our measure provides a direct quantification of the distance of the financial market from a critical state defined precisely as the limit of diverging trading activity in the absence of any external driving.
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Affiliation(s)
- Vladimir Filimonov
- Department of Management, Technology and Economics, ETH, Zürich, Switzerland.
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Gubiec T, Kutner R. Backward jump continuous-time random walk: an application to market trading. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:046119. [PMID: 21230357 DOI: 10.1103/physreve.82.046119] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/28/2010] [Revised: 08/27/2010] [Indexed: 05/30/2023]
Abstract
The backward jump modification of the continuous-time random walk model or the version of the model driven by the negative feedback was herein derived for spatiotemporal continuum in the context of a share price evolution on a stock exchange. In the frame of the model, we described stochastic evolution of a typical share price on a stock exchange with a moderate liquidity within a high-frequency time scale. The model was validated by satisfactory agreement of the theoretical velocity autocorrelation function with its empirical counterpart obtained for the continuous quotation. This agreement is mainly a result of a sharp backward correlation found and considered in this article. This correlation is a reminiscence of such a bid-ask bounce phenomenon where backward price jump has the same or almost the same length as preceding jump. We suggested that this correlation dominated the dynamics of the stock market with moderate liquidity. Although assumptions of the model were inspired by the market high-frequency empirical data, its potential applications extend beyond the financial market, for instance, to the field covered by the Le Chatelier-Braun principle of contrariness.
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Affiliation(s)
- Tomasz Gubiec
- Division of Physics Education, Institute of Experimental Physics, Faculty of Physics, University of Warsaw, Smyczkowa Str 5/7, PL-02678 Warsaw, Poland.
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