Relevant bibliographies by topics / Multifractal time series

Academic literature on the topic 'Multifractal time series'

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Published: 30 May 2022
Last updated: 31 May 2022

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Journal articles on the topic "Multifractal time series"

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Holdsworth, Amber M., Nicholas K. R. Kevlahan, and David J. D. Earn. "Multifractal signatures of infectious diseases." Journal of The Royal Society Interface 9, no. 74 (March 22, 2012): 2167–80. http://dx.doi.org/10.1098/rsif.2011.0886.

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Incidence of infection time-series data for the childhood diseases measles, chicken pox, rubella and whooping cough are described in the language of multifractals. We explore the potential of using the wavelet transform maximum modulus (WTMM) method to characterize the multiscale structure of the observed time series and of simulated data generated by the stochastic susceptible-exposed-infectious-recovered (SEIR) epidemic model. The singularity spectra of the observed time series suggest that each disease is characterized by a unique multifractal signature, which distinguishes that particular disease from the others. The wavelet scaling functions confirm that the time series of measles, rubella and whooping cough are clearly multifractal, while chicken pox has a more monofractal structure in time. The stochastic SEIR epidemic model is unable to reproduce the qualitative singularity structure of the reported incidence data: it is too smooth and does not appear to have a multifractal singularity structure. The precise reasons for the failure of the SEIR epidemic model to reproduce the correct multiscale structure of the reported incidence data remain unclear.
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Bakucz, Peter, and Gabor Kiss. "Modeling of probable maximum values in autonomous driving." SYSTEM THEORY, CONTROL AND COMPUTING JOURNAL 1, no. 2 (December 31, 2021): 58–64. http://dx.doi.org/10.52846/stccj.2021.1.2.28.

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In this paper, we approximate the probable maximum (very rare, extremal) values of highly autonomous driving sensor signals by reviewing two methods based on dynamic time series scaling and multifractal statistics.The article is a significantly revised and modified version of the conference material ("Determination of extreme values ​​in autonomous driving based on multifractals and dynamic scaling") presented at the conference "2021 IEEE 15th International Symposium on Applied Computational Intelligence and Informatics, SACI". The method of dynamic scaling is originally derived from statistical physics and approximates the critical interface phenomena. The time series of the vibration signal of the corner radar can be considered as a fractal surface and grow appropriately for a given scale-inverse dynamic equation. In the second method we initiate, that multifractal statistics can be useful in searching for statistical analog time series that have a similar multifractal spectrum as the original sensor time series.
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KLEMENT, STEPHAN, KARL W. KRATKY, and JOHANN NITTMANN. "PRACTICAL TIME-SERIES ANALYSIS WITH MULTIFRACTAL METHODS." Fractals 01, no. 03 (September 1993): 735–43. http://dx.doi.org/10.1142/s0218348x93000770.

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Time-series data of various origins are studied by analyzing their corresponding multifractal f(α)-spectral which are obtained by use of the so-called canonical method. The classes of data samples under investigation include: (a) airborne particle count data taken from an industrial cleanroom environment; (b) data generated by use of a (pseudo-)random number generator; and (c) data resulting from the iteration of the logistic map for the value r=4.0 of the control parameter, thus exhibiting chaotic behavior. From the resulting multifractal spectra, typical features of the f(α)-curve can be identified in relation to the corresponding class of original data. These findings can be of interest for various purposes. One application under consideration is the processing of microcontamination particle data recorded in high-quality cleanrooms. These are of great importance to the increasing miniaturization of semiconductor devices. In processing microcontamination particle data, the multifractal analysis can help to extract significant information from an enormous number of data to compress these data into a reasonable quantity. Another interesting aspect can be found in using the multifractal spectrum as a possible instrument for estimating the quality and performance of a random number generator.
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Figueirêdo, P. H., E. Nogueira, M. A. Moret, and Sérgio Coutinho. "Multifractal analysis of polyalanines time series." Physica A: Statistical Mechanics and its Applications 389, no. 10 (May 2010): 2090–95. http://dx.doi.org/10.1016/j.physa.2009.11.045.

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Li, Yun Fa. "Application of Multifractal Statistics Method on Time Series." Applied Mechanics and Materials 556-562 (May 2014): 4559–62. http://dx.doi.org/10.4028/www.scientific.net/amm.556-562.4559.

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The fluctuations observed in tokamaks, stellarators and linear machines were similar with turbulent plasma in fusion devices, which were stochastic system, and the application of statistics method on them is studied in depth. First, the relating theories were summarized; Second, the mathematical model of the multifractal process is analyzed; Finally, the simulation on multifractal analysis of plasma turbulence and financial time series is carried out, results show that this method can be applied in time series effectively.
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Tzanis, Chris G., Ioannis Koutsogiannis, Kostas Philippopoulos, and Nikolaos Kalamaras. "Multifractal Detrended Cross-Correlation Analysis of Global Methane and Temperature." Remote Sensing 12, no. 3 (February 7, 2020): 557. http://dx.doi.org/10.3390/rs12030557.

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Multifractal Detrended Cross-Correlation Analysis (MF-DCCA) was applied to time series of global methane concentrations and remotely-sensed temperature anomalies of the global lower and mid-troposphere, with the purpose of investigating the multifractal characteristics of their cross-correlated time series and examining their interaction in terms of nonlinear analysis. The findings revealed the multifractal nature of the cross-correlated time series and the existence of positive persistence. It was also found that the cross-correlation in the lower troposphere displayed more abundant multifractal characteristics when compared to the mid-troposphere. The source of multifractality in both cases was found to be mainly the dependence of long-range correlations on different fluctuation magnitudes. Multifractal Detrended Fluctuation Analysis (MF-DFA) was also applied to the time series of global methane and global lower and mid-tropospheric temperature anomalies to separately study their multifractal properties. From the results, it was found that the cross-correlated time series exhibit similar multifractal characteristics to the component time series. This could be another sign of the dynamic interaction between the two climate variables.
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Kalisky, Tomer, Yosef Ashkenazy, and Shlomo Havlin. "Volatility of fractal and multifractal time series." Israel Journal of Earth Sciences 56, no. 1 (December 1, 2007): 47–56. http://dx.doi.org/10.1560/ijes.56.1.47.

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Wang, Jeen-Hwa, and Chung-Wein Lee. "Multifractal Measures of Time Series of Earthquakes." Journal of Physics of the Earth 45, no. 5 (1997): 331–45. http://dx.doi.org/10.4294/jpe1952.45.331.

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Turiel, Antonio, and Conrad J. Pérez-Vicente. "Multifractal geometry in stock market time series." Physica A: Statistical Mechanics and its Applications 322 (May 2003): 629–49. http://dx.doi.org/10.1016/s0378-4371(02)01830-7.

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Xiong, Hui, and Pengjian Shang. "Weighted multifractal analysis of financial time series." Nonlinear Dynamics 87, no. 4 (November 10, 2016): 2251–66. http://dx.doi.org/10.1007/s11071-016-3187-1.

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Dissertations / Theses on the topic "Multifractal time series"

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Булах, В. А., Л. О. Кіріченко, and Т. А. Радівілова. "Classification of Multifractal Time Series by Decision Tree Methods." Thesis, КНУ, 2018. http://openarchive.nure.ua/handle/document/5840.

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The article considers classification task of model fractal time series by the methods of machine learning. To classify the series, it is proposed to use the meta algorithms based on decision trees. To modeling the fractal time series, binomial stochastic cascade processes are used. Classification of time series by the ensembles of decision trees models is carried out. The analysis indicates that the best results are obtained by the methods of bagging and random forest which use regression trees.
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Snguanyat, Ongorn. "Stochastic modelling of financial time series with memory and multifractal scaling." Queensland University of Technology, 2009. http://eprints.qut.edu.au/30240/.

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Financial processes may possess long memory and their probability densities may display heavy tails. Many models have been developed to deal with this tail behaviour, which reflects the jumps in the sample paths. On the other hand, the presence of long memory, which contradicts the efficient market hypothesis, is still an issue for further debates. These difficulties present challenges with the problems of memory detection and modelling the co-presence of long memory and heavy tails. This PhD project aims to respond to these challenges. The first part aims to detect memory in a large number of financial time series on stock prices and exchange rates using their scaling properties. Since financial time series often exhibit stochastic trends, a common form of nonstationarity, strong trends in the data can lead to false detection of memory. We will take advantage of a technique known as multifractal detrended fluctuation analysis (MF-DFA) that can systematically eliminate trends of different orders. This method is based on the identification of scaling of the q-th-order moments and is a generalisation of the standard detrended fluctuation analysis (DFA) which uses only the second moment; that is, q = 2. We also consider the rescaled range R/S analysis and the periodogram method to detect memory in financial time series and compare their results with the MF-DFA. An interesting finding is that short memory is detected for stock prices of the American Stock Exchange (AMEX) and long memory is found present in the time series of two exchange rates, namely the French franc and the Deutsche mark. Electricity price series of the five states of Australia are also found to possess long memory. For these electricity price series, heavy tails are also pronounced in their probability densities. The second part of the thesis develops models to represent short-memory and longmemory financial processes as detected in Part I. These models take the form of continuous-time AR(∞) -type equations whose kernel is the Laplace transform of a finite Borel measure. By imposing appropriate conditions on this measure, short memory or long memory in the dynamics of the solution will result. A specific form of the models, which has a good MA(∞) -type representation, is presented for the short memory case. Parameter estimation of this type of models is performed via least squares, and the models are applied to the stock prices in the AMEX, which have been established in Part I to possess short memory. By selecting the kernel in the continuous-time AR(∞) -type equations to have the form of Riemann-Liouville fractional derivative, we obtain a fractional stochastic differential equation driven by Brownian motion. This type of equations is used to represent financial processes with long memory, whose dynamics is described by the fractional derivative in the equation. These models are estimated via quasi-likelihood, namely via a continuoustime version of the Gauss-Whittle method. The models are applied to the exchange rates and the electricity prices of Part I with the aim of confirming their possible long-range dependence established by MF-DFA. The third part of the thesis provides an application of the results established in Parts I and II to characterise and classify financial markets. We will pay attention to the New York Stock Exchange (NYSE), the American Stock Exchange (AMEX), the NASDAQ Stock Exchange (NASDAQ) and the Toronto Stock Exchange (TSX). The parameters from MF-DFA and those of the short-memory AR(∞) -type models will be employed in this classification. We propose the Fisher discriminant algorithm to find a classifier in the two and three-dimensional spaces of data sets and then provide cross-validation to verify discriminant accuracies. This classification is useful for understanding and predicting the behaviour of different processes within the same market. The fourth part of the thesis investigates the heavy-tailed behaviour of financial processes which may also possess long memory. We consider fractional stochastic differential equations driven by stable noise to model financial processes such as electricity prices. The long memory of electricity prices is represented by a fractional derivative, while the stable noise input models their non-Gaussianity via the tails of their probability density. A method using the empirical densities and MF-DFA will be provided to estimate all the parameters of the model and simulate sample paths of the equation. The method is then applied to analyse daily spot prices for five states of Australia. Comparison with the results obtained from the R/S analysis, periodogram method and MF-DFA are provided. The results from fractional SDEs agree with those from MF-DFA, which are based on multifractal scaling, while those from the periodograms, which are based on the second order, seem to underestimate the long memory dynamics of the process. This highlights the need and usefulness of fractal methods in modelling non-Gaussian financial processes with long memory.
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Zhou, Xiaobo. "Fractal and Multifractal Analysis of Runoff Time Series and Stream Networks in Agricultural Watersheds." Diss., Virginia Tech, 2004. http://hdl.handle.net/10919/11287.

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The usefulness of watershed hydrological process models is considerably increased when they can be extrapolated across spatial and temporal scales. This scale transfer problem, meaning the description and prediction of characteristics and processes at a scale different from the one at which observations and measurements are made, and has become the subject of much current research in hydrology and other areas. Quantitative description of fractal scaling behavior of runoff and stream network morphometry in agricultural watersheds has not been previously reported. In the present study, fractal and multifractal scaling of daily runoff rate in four experimental agricultural watersheds and their associated sub-watersheds (32 in total) were investigated. The time series of daily runoff rate were obtained from the database (comprising about 16,600 station years of rainfall and runoff data for small agricultural watersheds across the U.S.) developed by the Hydrological and Remote Sensing Laboratory, Agricultural Research Service, US Department of Agriculture (HRSL/ARS/USDA). Fractal scaling patterns of the Digital Elevation Model (DEM)-extracted stream network morphometry for these four watersheds were also examined. The morphometry of stream networks of four watersheds were obtained by Geographic Information System (GIS) manipulation of digital elevation data downloaded from the most recent (July 2004) U.S. Geological Survey (USGS) National Elevation Dataset (NED). Several threshold values of contribution area for stream initiation were used to extract stream networks for each of the four watersheds. The principal measures of fractal scaling determined for the runoff series were the Hurst exponent obtained by rescaled range (R/S) analysis, the fractal dimension estimated by the shifted box-counting method, and the multifractal scaling function parameters (a and C1) of the Universal Multifractal Model (UMM). Corresponding measures for the DEM-extracted stream networks at each threshold value were the fractal dimension estimated using the box-counting technique and the Horton ratios of the network. Daily runoff rate exhibited strong long-term dependence and scale invariance over certain time scales. The same fractal dimensions and Hurst exponents were obtained for the sub-watersheds within each watershed. Runoff exhibited multifractal behavior that was well described by UMM. The multifractal parameters a (quantifies how far the process is from monofractality) and C1 (characterizes the sparseness or inhomogeneity of the mean of the process) were reasonably close to each other for sub-watersheds within a watershed and were generally similar among four watersheds. For the DEM-extracted networks, the morphometric attributes and Horton ratios as well as their fractal dimensions were dependent on the threshold values of contribution area used in the extraction process. The fractal dimensions were almost identical for DEM-extracted stream networks of the four watersheds. The DEM-extracted stream network displayed a single scaling pattern, rather than multifractal behavior. Explanation of the physical significance of fractal characteristics of the stream network in relation to runoff time series would require more data than were available in this study.
Ph. D.
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Nascimento, César Moura. "Análise multifractal e seções de Lévy de flutuações heterocedásticas." Universidade Federal de Alagoas, 2008. http://repositorio.ufal.br/handle/riufal/1012.

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An important problem in Physics concerns the study of stochastic processes and fluctuations away from the mean of dynamical variables. In a wide range of systems, some of the observed variables have a macroscopic quality, in the sense that they represent averages or sums over time or space of "microscopic" quantities. When long-range memory or correlation effects do not play a significant role, then the necessary and sufficient conditions for the Central Limit Theorem to hold can become satisfied. Quite often, the second moments of the studied dynamical variable do not diverge, hence in many important instances, the fluctuations of many systems follow Gaussian statistics. On the other hand, complex systems generate some variabilities that often deviate them from Gaussian statistics. Here, we focus on two properties related to Gaussian fluctuations: (i) monofractality and (ii) homoscedasticity. Specifically, we first address the general question about the nature of the relationship between multifractality and heteroscedasticity. We applied multifractal detrended fluctuation analysis to a nonstationary high frequency financial time series obtained from currency markets. As a second test, we applied the technique to the audio time series of Beethoven's fifth symphony. We obtained results suggesting that heteroscedasticity can cause or increase multifractality. We also investigate in greater detail the convergence to the homoskedastic and monofractal Gaussian regime, using the mathematical formalism of Lévy sections, as previously applied to time series. We report several conclusions related to these questions and discuss the generality of these results in the context of the physics of complex systems.
Conselho Nacional de Desenvolvimento Científico e Tecnológico
Um importante problema em Física está relacionado ao estudo de processos estocásticos e flutuações de variáveis dinâmicas. Em uma variedade de sistemas, algumas das variáveis observadas têm uma qualidade macroscópica, no sentido de que elas representam a média ou a soma sobre o espaço ou tempo de quantidades microscópicas. Quando efeitos de memória de longo alcance ou correlação não desempenharem um papel significativo, então as condições necessárias e suficientes para a validade do Teorema do Limite Central podem ser satisfeitas. Frequentemente o segundo momento da variável em questão não diverge. Consequentemente em muitos exemplos importantes, as flutuações de muitos sistemas seguem uma estatística Gaussiana. Em contraste, sistemas complexos geram flutuações que muitas vezes os desviam da estatística Gaussiana. Aqui, nós focamos em duas propriedades relacionadas à flutuações Gaussianas: (i) monofractalidade e (ii) homocedasticidade. Especificamente, discutimos primeiro a questão geral sobre a natureza da relação entre multifractalidade e heterocedasticidade. Aplicamos a multifractal detrended fluctuations analysis a uma série temporal financeira não estacionária e de alta freqüência referente à taxa cambial. Como um segundo teste, aplicamos a mesma técnica de análise para a série de áudio da quinta sinfonia de Beethoven. Obtivemos resultados que indicam que a heterocedasticidade pode causar ou aumentar a multifractalidade. Também investigamos em detalhes a convergência para o regime homocedástico e monofratal Gaussiano usando o método matemático de seções de Lévy, como previamente aplicado a séries temporais. Apresentamos conclusões relacionadas a estes questionamentos e discutimos a generalidade destes resultados no contexto da Física de sistemas complexos.
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Олемской, Александр Иванович, Олександр Іванович Олємской, Oleksandr Ivanovych Oliemskoi, and Э. Ф. Галимарданова. "Мультифрактальный анализ временных рядов." Thesis, Изд-во СумГУ, 2008. http://essuir.sumdu.edu.ua/handle/123456789/3954.

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Олемской, Александр Иванович, Олександр Іванович Олємской, Oleksandr Ivanovych Oliemskoi, Вадим Николаевич Борисюк, Вадим Миколайович Борисюк, and Vadym Mykolaiovych Borysiuk. "Мультифрактальный анализ самоподобных временных рядов." Thesis, Изд-во СумГУ, 2009. http://essuir.sumdu.edu.ua/handle/123456789/3886.

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Hoang, Cong Tuan. "Prise en compte des fluctuations spatio-temporelles pluies-débits pour une meilleure gestion de la ressource en eau et une meilleure évaluation des risques." Phd thesis, Université Paris-Est, 2011. http://pastel.archives-ouvertes.fr/pastel-00658537.

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Réduire la vulnérabilité et accroître la résilience des sociétés d'aujourd'hui aux fortes précipitations et inondations exige de mieux caractériser leur très forte variabilité spatio-temporelle observable sur une grande gamme d'échelle. Nous mettons donc en valeur tout au long de cette thèse l'intérêt méthodologique d'une approche multifractale comme étant la plus appropriée pour analyser et simuler cette variabilité. Cette thèse aborde tout d'abord le problème de la qualité des données, qui dépend étroitement de la résolution temporelle effective de la mesure, et son influence sur l'analyse multifractale et la détermination de lois d'échelle des processus de précipitations. Nous en soulignons les conséquences pour l'hydrologie opérationnelle. Nous présentons la procédure SERQUAL qui permet de quantifier cette qualité et de sélectionner les périodes correspondant aux critères de qualité requise. Un résultat surprenant est que les longues chronologies de pluie ont souvent une résolution effective horaire et rarement de 5 minutes comme annoncée. Ensuite, cette thèse se penche sur les données sélectionnées pour caractériser la structure temporelle et le comportement extrême de la pluie. Nous analysons les sources d'incertitudes dans les méthodes multifractales " classiques " d'estimation des paramètres et nous en déduisons des améliorations pour tenir compte, par exemple, de la taille finie des échantillons et des limites de la dynamique des capteurs. Ces améliorations sont utilisées pour obtenir les caractéristiques multifractales de la pluie à haute résolution de 5 minutes pour plusieurs départements de la France (à savoir, les départements 38, 78, 83 et 94) et pour aborder la question de l'évolution des précipitations durant les dernières décennies dans le cadre du changement climatique. Cette étude est confortée par l'analyse de mosaïques radars concernant trois événements majeurs en région parisienne. Enfin, cette thèse met en évidence une autre application des méthodes développées, à savoir l'hydrologie karstique. Nous discutons des caractéristiques multifractales des processus de précipitation et de débit à différentes résolutions dans deux bassins versant karstiques au sud de la France. Nous analysons, en utilisant les mesures journalière, 30 minutes et 3 minutes, la relation pluie-débit dans le cadre multifractal. Ceci est une étape majeure dans la direction d'une définition d'un modèle multi-échelle pluie-débit du fonctionnement des bassins versants karstiques
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Fonseca, Eder Lucio da. "O estudo das propriedades multifractais de séries temporais financeiras." Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/100/100132/tde-07052012-230908/.

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Séries temporais financeiras, como índices de mercado e preços de ativos, são produzidas por interações complexas dos agentes que participam do mercado. As propriedades fractais e multifractais destas séries fornecem evidências para detectar com antecedência a ocorrência de movimentos bruscos de mercado (crashes). Tais evidências são obtidas ao aplicar o conceito de Calor Específico Análogo C(q), proveniente da equivalência entre a Multifractalidade e Termodinâmica. Na proximidade de um crash, C(q) apresenta um ombro anômalo à direita de sua curva, enquanto que na ausência de um crash, possui o formato parecido com uma distribuição gaussiana. Com base neste comportamento, o presente trabalho propõe um novo indicador temporal IA(i), definido como a taxa de variação da área sob a curva de C(q). O indicador foi construído por intermédio de uma janela temporal de tamanho s que se movimenta ao longo da série, simulando a entrada de dados na série ao longo do tempo. A análise de IA(i) permite detectar com antecedência a ocorrência de grandes movimentos, como os famosos crashes de 1929 e 1987 para os índices Dow Jones, S&P500 e Nasdaq. Além disso, a análise simultânea de medidas como a Energia Livre, a Dimensão Multifractal e o Espectro Multifractal, sugerem que um crash de mercado se assemelha a uma transição de fase. A robustez do método para diferentes ativos e diferentes períodos de tempo, demonstra a importância dos resultados. Além disso, modelos estatísticos não lineares para a volatilidade foram empregados no trabalho para estudar grandes flutuações causadas por crashes e crises financeiras ao longo do tempo.
Financial time series such as market index and asset prices, are produced by complex interactions of agents that trade in the market. The fractal and multifractal properties of these series provides evidence for early detection of the occurrence of sudden market movements (crashes). This evidence is obtained by applying the concept of Analog Specific Heat C(q), from the equivalence between the Multifractal Analysis and Thermodynamics. In the vicinity of a crash, C(q) exhibits a shoulder at the right side of its curve, while in the absence of a crash, C(q) presents a form similar to a Gaussian distribution curve. Based on this behavior, it is proposed in this work a new temporal indicator IA(i) defined here as the area variation rate over the Specific Heat function. We have constructed the mentioned indicator from a window of data with the first points (size s), that moves throughout the series, simulating the actual input of data over time. The indicator IA(i) allows one detecting in advance the occurrence of large financial market movements, such as those occurred in 1929 and 1987 for the marked indexes Dow Jones, Nasdaq and S&P500. Moreover, the simultaneous analysis of measures such as the Free Energy, Multifractal Dimension and Multifractal Spectrum suggest that a market crash resembles a phase transition. The robustness of the method for others assets and different periods of time demonstrates the importance of the results. Moreover, nonlinear statistical models for volatility have been employed in the work to study large fluctuations caused by crashes and financial crises over time.
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Huang, Yongxiang. "ARBITRARY ORDER HILBERT SPECTRAL ANALYSIS DEFINITION AND APPLICATION TO FULLY DEVELOPED TURBULENCE AND ENVIRONMENTAL TIME SERIES." Phd thesis, Université des Sciences et Technologie de Lille - Lille I, 2009. http://tel.archives-ouvertes.fr/tel-00439605.

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La Décomposition Modale Empirique (Empirical Mode Decomposition - EMD) ou la Transformation de Hilbert-Huang (HHT) est une nouvelle méthode d'analyse temps-fréquence qui est particulièrement adaptée pour des séries temporelles nonlinéaires et non stationnaires. Cette méthode a été proposée par NE. HUANG. il y a plus de dix ans. Pendant les dix dernières années, plus de 1000 articles ont appliqué cette méthode dans le cadre de diverses applications ou domaines de recherche. Dans cette thèse, nous appliquons cette méthode à des séries temporelles de turbulence, pour la première fois, et à des séries temporelles environnementales. Nous avons obtenu comme résultat le fait que la méthode EMD correspond à un banc de filtre dyadique (ou quasi-dyadique) pour la turbulence pleinement développée. Pour caractériser les propriétés intermittentes d'une série temporelle invariante d'échelle, nous avons généralisé l'analyse spectrale de Hilbert-Huang classique à des moments d'ordre arbitraire $q$, pour effectuer ce que nous avons appelé ``analyse spectrale de Hilbert d'ordre arbitraire''. Ceci fournit un nouveau cadre pour analyser l'invariance d'échelle directement dans un espace amplitude-fréquence, en estimant une intégrale marginale d'une pdf jointe $p(\omega,\mathcal{A})$ de la fréquence instantanée $\omega$ et de l'amplitude $\mathcal{A}$. Nous validons tout d'abord la méthode en analysant des séries temporelles de mouvement Brownien fractionnaire, et en analysant des séries temporelles multifractales synthétiques, en tant que modèle respectivement de processus monofractals et multifractals. Nous comparons les résultats obtenus avec la nouvelle méthode, à l'analyse classique utilisant les fonctions de structure: nous trouvons numériquement que la méthodologie utilisant l'approche de Hilbert fournit un estimateur plus précis pour le paramètre d'intermittence. Avec une hypothèse de stationarité, nous proposons un modèle analytique pour la fonction d'autocorrélation des incréments de séries temporelles de vitesse $\Delta u_{\ell}(t)$, où $\Delta u_{\ell}(t)=u(t+\ell)-u(t)$, et $\ell$ est l'incrément temporel. Dans le cadre de ce modèle, nous prouvons analytiquement que, si une loi de puissance est valide pour la série d'origine, la position minimisant la fonction d'autocorrélation de la variable d'origine est égale exactement au temps de séparation $\ell$ lorsque $\ell$ appartient à la zone invariante d'échelle. Ce modèle prédit une loi de puissance pour la valeur minimum, comportement vérifié par une simulation de mouvement Brownien fractionnaire et à partir de données expérimentales de turbulence. En introduisant une fonction cumulative pour la fonction d'autocorrélation, la contribution en échelle est alors caractérisée dans l'espace de fréquence de Fourier. Nous observons que la contribution principale à la fonction d'autocorrélation provient des grandes échelles. La même idée est appliquée à la fonction de structure d'ordre 2. Nous obtenons que celle-ci est également fortement influencée par les grandes échelles, ce qui montre que ceci n'est pas une bonne approche pour extraire les exposants invariants d'échelle d'une série temporelle lorsque les données sont caractérisées par des grandes échelles énergétiques. Nous appliquons ensuite cette méthodologie Hilbert-Huang à une base de données de turbulence homogène et presque isotrope, pour caractériser les propriétés multifractales invariantes d'échelle des série temporelles de vitesse en turbulence pleinement développée. Nous obtenons un comportement invariant d'échelle pour la pdf jointe $p(\omega,\mathcal{A})$ avec un exposant proche de la valeur de Kolmogorov. Nous estimons les exposants $\zeta(q)$ dans un espace amplitude-fréquence, pour la première fois. L'hypothèse d'isotropie est testée échelle par échelle dans l'espace amplitude-fréquence. Nous obtenons que le rapport d'isotropie généralisé décroit linéairement avec le moment $q$. Nous effectuons également l'analyse d'une série temporelle de température (scalaire passif) possédant un effet de rampe marqué (ramp-cliff). Pour ces données, l'approche traditionnelle utilisant les fonctions de structure ne fonctionne pas. Mais la nouvelle méthode développée dans cette thèse fournit un net régime invariant d'échelle jusqu'au moment $q=8$. Les exposants $\xi_{\theta}(q)-1$ sont très proches des exposants $\zeta(q)$ obtenus par l'approche des fonctions de structure pour la vitesse longitudinale. Nous nous intéressons ensuite à l'auto-similarité étendue (Extended Self Similarity - ESS) dans le cadre Hilbert-Huang. En ce qui concerne la méthode ESS, qui est devenue classique en turbulence, nous adaptons l'approche pour le cas Hilbert-Huang dans un espace de fréquence, et nous constatons que le modèle lognormal, avec un coefficient adéquat, fournit une très bonne estimation des exposants invariants d'échelle. Finalement nous appliquons la nouvelle méthodologie à des données environnementales: des débits de rivières, et des données de turbulence marine dans la zone de surf. Dans ce dernier cas, la méthode ESS permet de séparer les ondes de vent de la turbulence à petite échelle.
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Булах, В. А., Л. О. Кіріченко, and Т. А. Радівілова. "Time Series Classification Based on Fractal Properties." Thesis, 2018. http://openarchive.nure.ua/handle/document/9452.

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The article considers classification task of fractal time series by the meta algorithms based on decision trees. Binomial multiplicative stochastic cascades are used as input time series. Comparative analysis of the classification approaches based on different features is carried out. The results indicate the advantage of the machine learning methods over the traditional estimating the degree of self-similarity.
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Books on the topic "Multifractal time series"

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Sattarhoff, Cristina. Statistical Inference in Multifractal Random Walk Models for Financial Time Series. Lang GmbH, Internationaler Verlag der Wissenschaften, Peter, 2011.

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Sattarhoff, Cristina. Statistical Inference in Multifractal Random Walk Models for Financial Time Series. Lang GmbH, Internationaler Verlag der Wissenschaften, Peter, 2012.

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Lux, Thomas, and Mawuli Segnon. Multifractal Models in Finance. Edited by Shu-Heng Chen, Mak Kaboudan, and Ye-Rong Du. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780199844371.013.8.

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This chapter provides an overview over the recently developed so-called multifractal (MF) approach for modeling and forecasting volatility. For analysts and policy makers, volatility is a key variable for understanding market fluctuations. Analysts need accurate forecasts of volatility for tasks such as risk management, as well as option and futures pricing. In addition, asset market volatility plays an important role in monetary policy. The chapter, then, outlines the genesis of the multifractal approach from similar models of turbulent flows in statistical physics and provides details about different specifications of multifractal time series models in finance, available methods for their estimation, and the current state of their empirical applications.
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Book chapters on the topic "Multifractal time series"

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Kantelhardt, Jan W. "Fractal and Multifractal Time Series." In Mathematics of Complexity and Dynamical Systems, 463–87. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-1806-1_30.

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Kantelhardt, Jan W. "Fractal and Multifractal Time Series." In Encyclopedia of Complexity and Systems Science, 3754–79. New York, NY: Springer New York, 2009. http://dx.doi.org/10.1007/978-0-387-30440-3_221.

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Kantelhardt, Jan W. "Fractal and Multifractal Time Series." In Encyclopedia of Complexity and Systems Science, 1–37. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-642-27737-5_221-3.

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Ivanova, Kristinka. "Time Series Analysis of Microwave Signals: Multifractal Aspects." In Nano-Crystalline and Thin Film Magnetic Oxides, 283–92. Dordrecht: Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-011-4493-3_23.

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Jizba, Petr, and Jan Korbel. "Modeling Financial Time Series: Multifractal Cascades and Rényi Entropy." In Emergence, Complexity and Computation, 227–36. Berlin, Heidelberg: Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-642-45438-7_22.

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Bouchaud, Jean-Philippe, and Jean-François Muzy. "Financial Time Series: From Batchelier’s Random Walks to Multifractal ‘Cascades’." In Lecture Notes in Physics, 229–46. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-540-39668-0_11.

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Jizba, Petr, and Jan Korbel. "Applications of Multifractal Diffusion Entropy Analysis to Daily and Intraday Financial Time Series." In ISCS 2014: Interdisciplinary Symposium on Complex Systems, 333–42. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-10759-2_34.

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Muñoz-Diosdado, A., and A. M. Aguilar-Molina. "Curvature Analysis of Multifractal Spectra for Time Series of RR Intervals for Patients with Congestive Heart Failure." In IFMBE Proceedings, 49–52. Singapore: Springer Singapore, 2015. http://dx.doi.org/10.1007/978-981-10-0266-3_10.

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Bogachev, Mikhail I., Naiming Yuan, and Armin Bunde. "Fractals and Multifractals in Geophysical Time Series." In Fractals, 231–71. Boca Raton, FL : CRC Press, Taylor & Francis Group, 2017. | “A science publishers book.”: CRC Press, 2017. http://dx.doi.org/10.1201/9781315152264-9.

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Banerjee, Santo, M. K. Hassan, Sayan Mukherjee, and A. Gowrisankar. "Fractal and Multifractal in Stochastic Time Series." In Fractal Patterns in Nonlinear Dynamics and Applications, 129–51. CRC Press, 2020. http://dx.doi.org/10.1201/9781315151564-5.

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Conference papers on the topic "Multifractal time series"

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Muñoz-Diosdado, A. "Multifractal Analysis of Time Series." In MODELING OF COMPLEX SYSTEMS: Seventh Granada Lectures. AIP, 2003. http://dx.doi.org/10.1063/1.1571344.

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Yuan, Ying, and Xin-tian Zhuang. "Multifractal Statistical Analysis of Financial Time Series." In 2006 International Conference on Machine Learning and Cybernetics. IEEE, 2006. http://dx.doi.org/10.1109/icmlc.2006.258580.

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Gospodinova, Evgeniya. "Time Series Analysis Using Fractal and Multifractal Methods." In CompSysTech '19: 20th International Conference on Computer Systems and Technologies. New York, NY, USA: ACM, 2019. http://dx.doi.org/10.1145/3345252.3345265.

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Zeng, Ming, Xiaonei Zhang, Jinghai Li, and Qinghao Meng. "Multiscale multifractal analysis of near-surface wind speed time series." In 2016 12th World Congress on Intelligent Control and Automation (WCICA). IEEE, 2016. http://dx.doi.org/10.1109/wcica.2016.7578757.

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Muñoz D., Alejandro. "Multifractal Analysis of Aging and Complexity in Heartbeat Time Series." In MEDICAL PHYSICS: Eighth Mexican Symposium on Medical Physics. AIP, 2004. http://dx.doi.org/10.1063/1.1811846.

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Yang, Yujun, Yimei Yang, and Jianping Li. "Role of mean in the multifractal analysis of financial time series." In 2017 14th International Computer Conference on Wavelet Active Media Technology and Information Processing (ICCWAMTIP). IEEE, 2017. http://dx.doi.org/10.1109/iccwamtip.2017.8301452.

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Jovanović, Gordana, Svetlana Stanišić, and Mirjana Perišić. "Multifractal Characteristics of Criteria Air Pollutant Time Series in Urban Areas." In Sinteza 2020. Beograd, Serbia: Singidunum University, 2020. http://dx.doi.org/10.15308/sinteza-2020-29-34.

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Domingues, Omar D., Philippe Ciuciu, Daria La Rocca, Patrice Abry, and Herwig Wendt. "Multifractal Analysis for Cumulant-Based Epileptic Seizure Detection in Eeg Time Series." In 2019 IEEE 16th International Symposium on Biomedical Imaging (ISBI). IEEE, 2019. http://dx.doi.org/10.1109/isbi.2019.8759288.

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Munoz-Diosdado, A., and J. L. Del Rio-Correa. "Further Study of the Asymmetry for Multifractal Spectra of Heartbeat Time Series." In Conference Proceedings. Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE, 2006. http://dx.doi.org/10.1109/iembs.2006.260166.

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Munoz-Diosdado, A., and J. L. Del Rio-Correa. "Further Study of the Asymmetry for Multifractal Spectra of Heartbeat Time Series." In Conference Proceedings. Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE, 2006. http://dx.doi.org/10.1109/iembs.2006.4397685.

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Reports on the topic "Multifractal time series"

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Derbentsev, V., A. Ganchuk, and Володимир Миколайович Соловйов. Cross correlations and multifractal properties of Ukraine stock market. Politecnico di Torino, 2006. http://dx.doi.org/10.31812/0564/1117.

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Recently the statistical characterizations of financial markets based on physics concepts and methods attract considerable attentions. The correlation matrix formalism and concept of multifractality are used to study temporal aspects of the Ukraine Stock Market evolution. Random matrix theory (RMT) is carried out using daily returns of 431 stocks extracted from database time series of prices the First Stock Trade System index (www.kinto.com) for the ten-year period 1997-2006. We find that a majority of the eigenvalues of C fall within the RMT bounds for the eigenvalues of random correlation matrices. We test the eigenvalues of C within the RMT bound for universal properties of random matrices and find good agreement with the results for the Gaussian orthogonal ensemble of random matrices—implying a large degree of randomness in the measured cross-correlation coefficients. Further, we find that the distribution of eigenvector components for the eigenvectors corresponding to the eigenvalues outside the RMT bound display systematic deviations from the RMT prediction. We analyze the components of the deviating eigenvectors and find that the largest eigenvalue corresponds to an influence common to all stocks. Our analysis of the remaining deviating eigenvectors shows distinct groups, whose identities correspond to conventionally identified business sectors. Comparison with the Mantegna minimum spanning trees method gives a satisfactory consent. The found out the pseudoeffects related to the artificial unchanging areas of price series come into question We used two possible procedures of analyzing multifractal properties of a time series. The first one uses the continuous wavelet transform and extracts scaling exponents from the wavelet transform amplitudes over all scales. The second method is the multifractal version of the detrended fluctuation analysis method (MF-DFA). The multifractality of a time series we analysed by means of the difference of values singularity stregth (or Holder exponent) ®max and ®min as a suitable way to characterise multifractality. Singularity spectrum calculated from daily returns using a sliding 250 day time window in discrete steps of 1. . . 10 days. We discovered that changes in the multifractal spectrum display distinctive pattern around significant “drawdowns”. Finally, we discuss applications to the construction of crushes precursors at the financial markets.
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Соловйов, Володимир Миколайович, and О. А. Сердюк. Мультифрактальний аналіз кризових явищ на фондових ринках. Видавець Ткачук О. В., 2015. http://dx.doi.org/10.31812/0564/1159.

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The work carried out multifractal analysis of the crisis on the stock markets today. It is shown that in the case of time series analysis and complex networks that are obtained by their special converting multifractal analysis indicates a marked increase in the complexity of the system during the crisis. This is evident through the expansion of singularity and growth collective and synchronization modes.
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Soloviev, Vladimir, Natalia Moiseienko, and Olena Tarasova. Modeling of cognitive process using complexity theory methods. [б. в.], 2019. http://dx.doi.org/10.31812/123456789/3609.

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The features of modeling of the cognitive component of social and humanitarian systems have been considered. An example of using multiscale, multifractal and network complexity measures has shown that these and other synergetic models and methods allow us to correctly describe the quantitative differences of cognitive systems. The cognitive process is proposed to be regarded as a separate implementation of an individual cognitive trajectory, which can be represented as a time series and to investigate its static and dynamic features by the methods of complexity theory. Prognostic possibilities of the complex systems theory will allow to correct the corresponding pedagogical technologies.
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Соловйов, Володимир Миколайович, Наталя Володимирівна Моісеєнко, and Олена Юріївна Тарасова. Complexity theory and dynamic characteristics of cognitive processes. Springer, January 2020. http://dx.doi.org/10.31812/123456789/4143.

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The features of modeling of the cognitive component of social and humanitarian systems have been considered. An example of using entropy multiscale, multifractal, recurrence and network complexity measures has shown that these and other synergetic models and methods allow us to correctly describe the quantitative differences of cognitive systems. The cognitive process is proposed to be regarded as a separate implementation of an individual cognitive trajectory, which can be represented as a time series and to investigate its static and dynamic features by the methods of complexity theory. Prognostic possibilities of the complex systems theory will allow to correct the corresponding pedagogical technologies. It has been proposed to track and quantitatively describe the cognitive trajectory using specially transformed computer games which can be used to test the processual characteristics of thinking.
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Nechaev, V., Володимир Миколайович Соловйов, and A. Nagibas. Complex economic systems structural organization modelling. Politecnico di Torino, 2006. http://dx.doi.org/10.31812/0564/1118.

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One of the well-known results of the theory of management is the fact, that multi-stage hierarchical organization of management is unstable. Hence, the ideas expressed in a number of works by Don Tapscott on advantages of network organization of businesses over vertically integrated ones is clear. While studying the basic tendencies of business organization in the conditions of globalization, computerization and internetization of the society and the results of the financial activities of the well-known companies, the authors arrive at the conclusion, that such companies, as IBM, Boeing, Mercedes-Benz and some others companies have not been engaged in their traditional business for a long time. Their partner networks performs this function instead of them. The companies themselves perform the function of system integrators. The Tapscott’s idea finds its confirmation within the framework of a new powerful direction of the development of the modern interdisciplinary science – the theory of the complex networks (CN) [2]. CN-s are multifractal objects, the loss of multifractality being the indicator of the system transition from more complex state into more simple state. We tested the multifractal properties of the data using the wavelet transform modulus maxima approach in order to analyze scaling properties of our company. Comparative analysis of the singularity spectrumf(®), namely, the difference between maximum and minimum values of ® (∆ = ®max ¡ ®min) shows that IBM company is considerably more fractal in comparison with Apple Computer. Really, for it the value of ∆ is equal to 0.3, while for the vertically integrated company Apple it only makes 0.06 – 5 times less. The comparison of other companies shows that this dependence is of general character. Taking into consideration the fact that network organization of business has become dominant in the last 5-10 years, we carried out research for the selected companies in the earliest possible period of time which was determined by the availability of data in the Internet, or by historically later beginning of stock trade of computer companies. A singularity spectrum of the first group of companies turned out to be considerably narrower, or shifted toward the smaller values of ® in the pre-network period. The latter means that dynamic series were antipersistant. That is, these companies‘ management was rigidly controlled while the impact of market mechanisms was minimized. In the second group of companies if even the situation did changed it did not change for the better. In addition, we discuss applications to the construction of portfolios of stock that have a stable ratio of risk to return.
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