Journal articles: 'Detrended fractal analysis'

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Qiu, Xiao Hong, Yong Bo Tan, and Bo Li. "Fractal Analysis of the Optimal Objective Function." Applied Mechanics and Materials 519-520 (February 2014): 811–15. http://dx.doi.org/10.4028/www.scientific.net/amm.519-520.811.

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The fractals of the optimization problems are first discussed. The multi-fractal parameters of the optimal objective function are computed by the Detrended Fluctuation Analysis (DFA) method. The multi-fractal general Hurst Index is related to the difficulty to solve the optimization problem. These features are verified by analyzing the first six test functions proposed on 2005 IEEE Congress on Evolutionary Computation. The results show that the different objective functions have obvious different multifractal and the general Hurst Index can be used to evaluate the difficulty to solve the optimization problem.

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Zhang, Xi, Xu Wu, Linlin Zhang, and Zhonglu Chen. "The Evaluation of Mean-Detrended Cross-Correlation Analysis Portfolio Strategy for Multiple risk Assets." Evaluation Review 46, no. 2 (February 3, 2022): 138–64. http://dx.doi.org/10.1177/0193841x221078642.

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The fractal characteristics of the security market were considered in portfolio strategy optimization. First, the detrended cross-correlation analysis was adopted to measure the fractal correlation of different securities. Second, the fractal correlation was embedded into the mean-variance criterion of the modern portfolio theory. Third, the mean-detrended cross-correlation analysis portfolio strategy of multiple risk assets was constructed, and the analytic solution of the strategy was given. Finally, the evaluation results revealed that the constructed the mean-detrended cross-correlation analysis portfolio strategy clearly improved investment performance, thus achieving the goal of optimizing the multiple risk asset portfolio strategy.

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Cabrera-Brito, Laura, German Rodriguez, Luis García-Weil, Mercedes Pacheco, Esther Perez, and Joanna J. Waniek. "Fractal Analysis of Deep Ocean Current Speed Time Series." Journal of Atmospheric and Oceanic Technology 34, no. 4 (April 2017): 817–27. http://dx.doi.org/10.1175/jtech-d-16-0098.1.

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AbstractFractal properties of deep ocean current speed time series, measured at a single-point mooring on the Madeira Abyssal Plain at 1000- and 3000-m depth, are explored over the range between one week and 5 years, by using the detrended fluctuation analysis and multifractal detrended fluctuation analysis methodologies. The detrended fluctuation analysis reveals the existence of two subranges with different scaling behaviors. Long-range temporal correlations following a power law are found in the time-scale range between approximately 50 days and 5 years, while a Brownian motion–type behavior is observed for shorter time scales. The multifractal analysis approach underlines a multifractal structure whose intensity decreases with depth. The analysis of the shuffled and surrogate versions of the original time series shows that multifractality is mainly due to long-range correlations, although there is a weak nonlinear contribution at 1000-m depth, which is confirmed by the detrended fluctuation analysis of volatility time series.

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ZHANG, JUNHUAN, and JUN WANG. "FRACTAL DETRENDED FLUCTUATION ANALYSIS OF CHINESE ENERGY MARKETS." International Journal of Bifurcation and Chaos 20, no. 11 (November 2010): 3753–68. http://dx.doi.org/10.1142/s0218127410028082.

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In this paper, we analyze and compare long-range power-law correlations of returns, absolute returns, squared returns, cubed returns and square waved returns for sixteen individual stocks from the block of energy sources of Chinese stock market and five stock indices (Shanghai Composite Index, Shenzhen Component Index, Dow Jones Industrial Average index, Nasdaq Composite Index, the Standard and Poor's 500 Index) by using a detrended fluctuation analysis approach. The empirical evidence suggests that Shanghai Composite Index is very close to Shenzhen Component Index and Nasdaq, DJIA is very close to S&P 500 in all cases. And the exponent trends of the returns are close to that of square waved returns. Also, five indices deviate from other sixteen individual energy stocks in all cases except square waved returns. Further, there are long-range correlations and persistence in volatility series of absolute returns and squared returns. Moreover, we investigate the long-term memory of these returns by applying Lo's modified rescaled range statistic. We find that the China energy market exhibits fractal and persistence properties.

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KONG, QINGGE, QING YU, MEIFENG DAI, YUE ZONG, XIAODONG WANG, JIANZHONG JIANG, and HUOJUN RUAN. "MULTIFRACTAL DETRENDED FLUCTUATION ANALYSIS BASED ON PSEUDO-BILINEAR FRACTAL INTERPOLATION FUNCTIONS ON METALLIC GLASSES." Fractals 26, no. 04 (August 2018): 1850047. http://dx.doi.org/10.1142/s0218348x18500470.

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Based on the multifractal detrended cross-correlation analysis, which is the most effective way to detect long-range cross-correlation of time series, in this paper, we present a new method called multifractal detrended fluctuation analysis based on pseudo-bilinear fractal interpolation functions (MFDFA-PBFIF). In order to get a better detrended effect, we replace the polynomial fitting with PBFIFs in detrended process, and the result shows that the MFDFA-PBFIF can achieve a more accurate result. Then, we analyze the Legendre spectrum to detect the multifractal property on metallic glasses with MFDFA-PBFIF.

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Zhang, Daoming, Cong Wang, Chuangye Li, and Wei Dai. "Multi-fractal detrended fluctuation half-spectrum analysis of HRV." Journal of Engineering 2019, no. 22 (November 1, 2019): 8315–18. http://dx.doi.org/10.1049/joe.2019.1067.

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Tu, Tongbi, Ali Ercan, and M. Levent Kavvas. "Fractal scaling analysis of groundwater dynamics in confined aquifers." Earth System Dynamics 8, no. 4 (October 24, 2017): 931–49. http://dx.doi.org/10.5194/esd-8-931-2017.

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Abstract. Groundwater closely interacts with surface water and even climate systems in most hydroclimatic settings. Fractal scaling analysis of groundwater dynamics is of significance in modeling hydrological processes by considering potential temporal long-range dependence and scaling crossovers in the groundwater level fluctuations. In this study, it is demonstrated that the groundwater level fluctuations in confined aquifer wells with long observations exhibit site-specific fractal scaling behavior. Detrended fluctuation analysis (DFA) was utilized to quantify the monofractality, and multifractal detrended fluctuation analysis (MF-DFA) and multiscale multifractal analysis (MMA) were employed to examine the multifractal behavior. The DFA results indicated that fractals exist in groundwater level time series, and it was shown that the estimated Hurst exponent is closely dependent on the length and specific time interval of the time series. The MF-DFA and MMA analyses showed that different levels of multifractality exist, which may be partially due to a broad probability density distribution with infinite moments. Furthermore, it is demonstrated that the underlying distribution of groundwater level fluctuations exhibits either non-Gaussian characteristics, which may be fitted by the Lévy stable distribution, or Gaussian characteristics depending on the site characteristics. However, fractional Brownian motion (fBm), which has been identified as an appropriate model to characterize groundwater level fluctuation, is Gaussian with finite moments. Therefore, fBm may be inadequate for the description of physical processes with infinite moments, such as the groundwater level fluctuations in this study. It is concluded that there is a need for generalized governing equations of groundwater flow processes that can model both the long-memory behavior and the Brownian finite-memory behavior.

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Wan, Li, Peng Chen, and Zhao Xian Gong. "Quantifying Fractal Dynamics of Metallogenic Systems with Detrended Fluctuation Analysis." Applied Mechanics and Materials 249-250 (December 2012): 26–30. http://dx.doi.org/10.4028/www.scientific.net/amm.249-250.26.

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In this paper, we analysed fractional dynamics behavior in metallogenic elements grade series, using detrended fluctuation analysis (DFA), with the objective to explore and understand the underlying dynamic mechanism. Our results show that the metallogenic elements grade series are the scale invariance and the long-range correlation. As in the case of element grade dynamics, the DFA scaling exponents can be used to discriminate mineral intensity.

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Li, Zhongwei, and You-Kuan Zhang. "Quantifying fractal dynamics of groundwater systems with detrended fluctuation analysis." Journal of Hydrology 336, no. 1-2 (March 2007): 139–46. http://dx.doi.org/10.1016/j.jhydrol.2006.12.017.

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Arsac, Laurent M., and Véronique Deschodt-Arsac. "Detrended fluctuation analysis in a simple spreadsheet as a tool for teaching fractal physiology." Advances in Physiology Education 42, no. 3 (September 1, 2018): 493–99. http://dx.doi.org/10.1152/advan.00181.2017.

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Fractal physiology demonstrated growing interest over the last decades among physiologists, neuroscientists, and clinicians. Many physiological systems coordinate themselves for reducing variability and maintain a steady state. When recorded over time, the output signal exhibits small fluctuations around a stable value. It is becoming increasingly clear that these fluctuations, in most free-running healthy systems, are not simply due to uncorrelated random errors and possess interesting properties, one of which is the property of fractal dynamics. Fractal dynamics model temporal processes in which similar patterns occur across multiple timescales of measurement. Smaller copies of a pattern are nested within larger copies of the pattern, a property termed scale invariance. It is an intriguing process that may deserve attention for implementing curricular development for students to reconsider homeostasis. Teaching fractal dynamics needs to make calculating resources available for students. The present paper offers a calculating resource that uses a basic formula and is executable in a simple spreadsheet. The spreadsheet allows computing detrended fluctuation analysis (DFA), the most frequently used method in the literature to quantify the fractal-scaling index of a physiological time series. DFA has been nicely described by the group at Harvard that designed it; the authors made the C language source available. Going further, it is suggested here that a guide to build DFA step by step in a spreadsheet has many advantages for teaching fractal physiology and beyond: 1) it promotes the DIY (do-it-yourself) in students and highlights scaling concepts; and 2) it makes DFA available for people not familiarized with executing code in C language.

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Nian, Da, and Zuntao Fu. "Extended self-similarity based multi-fractal detrended fluctuation analysis: A novel multi-fractal quantifying method." Communications in Nonlinear Science and Numerical Simulation 67 (February 2019): 568–76. http://dx.doi.org/10.1016/j.cnsns.2018.07.034.

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DAI, MEIFENG, YUE ZONG, XIAOQIAN WANG, WEIYI SU, YU SUN, and JIE HOU. "EFFECTS OF FRACTAL INTERPOLATION FILTER ON MULTIFRACTAL ANALYSIS." Fractals 25, no. 02 (April 2017): 1750024. http://dx.doi.org/10.1142/s0218348x17500244.

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Fractal interpolation filter is proposed for the first time in the literatures to transform original signals. Using the multifractal detrended fluctuation analysis (MFDFA), the authors investigate how the filter affects the multifractal scaling properties for both artificial and traffic signals. Specifically, the authors compare the multifractal scaling properties of signals before and after the transforms. It is shown that the fractal interpolation filter changes slightly the maximum value of the multifractal spectrum, while the values of spectrum width and maximum point of spectrum are much more affected by vertical scaling factor. The multifractal spectrum shrinks dramatically after the fractal interpolation filter. The fractal exponents in the signal change dramatically for the negative values of vertical scaling factor while remain stable otherwise. Thus, an appropriate vertical scaling factor can be found in order to minimize the effects of filter when one uses the fractal interpolation filter.

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Zuo, Shun Gen. "Multi-Fractal Nature of HS 300 Index and its Traded Volume." Advanced Materials Research 629 (December 2012): 796–800. http://dx.doi.org/10.4028/www.scientific.net/amr.629.796.

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A study of the multi-fractal nature of three time series related to the Hushen300 index, HS300, including daily closing prices, daily yield rates and daily traded volumes time series is presented. Multi-fractal Detrended Fluctuation Analysis (MFDFA) is used in the study. The results show that the three related time series are with strong persistence characters. By multi-fractal spectrum analysis, the width of the multi-fractal Spectra of traded volume series is to be found the biggest among the three. It means that the traded volumes series are most irregular.

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DU, GUAN, PENGJIAN SHANG, and XIAOJUN ZHAO. "MULTISCALE DETRENDED FLUCTUATION ANALYSIS OF TRAFFIC INDEX SERIES." Fluctuation and Noise Letters 13, no. 01 (March 2014): 1450001. http://dx.doi.org/10.1142/s0219477514500011.

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In this paper, we present a multiscale detrended fluctuation analysis (DFA) for describing the traffic fractal dynamics with a spectrum of scale exponents, a(s), rather than by a model of lumped parameters a1 and a2. The method combines DFA with moving fitting window to analyze the traffic index (TI) series in different scales, shows more details of scale properties and provides a reliable analysis. We also quantify the effects of weather, traffic peaks and traffic control on exponent spectra a(s). The results indicate clearly that at large scales, the exponents show large volatility and they all have their own exponent patterns. In addition, for the effect of traffic control, the scale exponents of traffic control are continuously obviously larger than those without traffic control at small scales. The multiscale DFA method provides new ways to measure the TI series and distinguishes groups in different conditions.

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Uning, R., N. A. Abu Osman, J. Usman, and W. A. B. Wan Abas. "Fractal Characterization of Gait in Parkinson's Disease Using Detrended Fluctuation Analysis." Journal of Biomechanics 40 (January 2007): S82. http://dx.doi.org/10.1016/s0021-9290(07)70079-9.

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EINSTEIN, ANDREW J., HAI-SHAN WU, and JUAN GIL. "DETRENDED FLUCTUATION ANALYSIS OF CHROMATIN TEXTURE FOR DIAGNOSIS IN BREAST CYTOLOGY." Fractals 10, no. 01 (March 2002): 19–25. http://dx.doi.org/10.1142/s0218348x02000999.

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Chromatin appearance in breast epithelial cells has been shown to have fractal properties, and detrended fluctuation analysis (DFA) is an effective method for characterizing the scaling in non-stationary fractal signals in terms of a scaling exponent. This study examines the use of DFA for the characterization of chromatin appearance in breast epithelial cells. Images of nuclei representative of fine-needle aspiration biopsies of the breast are characterized in terms of the scaling exponent for 19 patients with benign lesions and 22 patients with invasive ductal carcinoma. Characterizing patients by the standard deviations of the values of the scaling exponent for their representative nuclei, a statistically significant difference is noted between benign and malignant cases. This reflects that malignancies exhibit less variability in chromatin roughness than do benign cases. Previous logistic regression models for the diagnosis of breast epithelial cell lesions are improved upon by incorporating the standard deviation of the scaling exponent. Using leave-one-out cross-validation, the best logistic regression classifiers demonstrate a sensitivity of 95% and a specificity of 100%. A combination of DFA and lacunarity analysis is seen to provide the best approach to characterizing chromatin in breast epithelial cell nuclei.

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Wawrzaszek, Anna, Renata Modzelewska, Agata Krasińska, Agnieszka Gil, and Vasile Glavan. "Fractal Dimension Analysis of Earth Magnetic Field during 26 August 2018 Geomagnetic Storm." Entropy 24, no. 5 (May 14, 2022): 699. http://dx.doi.org/10.3390/e24050699.

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We analyse the fractal nature of geomagnetic field northward and eastward horizontal components with 1 min resolution measured by the four stations Belsk, Hel, Sodankylä and Hornsund during the period of 22 August–1 September, when the 26 August 2018 geomagnetic storm appeared. To reveal and to quantitatively describe the fractal scaling of the considered data, three selected methods, structure function scaling, Higuchi, and detrended fluctuation analysis are applied. The obtained results show temporal variation of the fractal dimension of geomagnetic field components, revealing differences between their irregularity (complexity). The values of fractal dimension seem to be sensitive to the physical conditions connected with the interplanetary shock, the coronal mass ejection, the corotating interaction region, and the high-speed stream passage during the storm development. Especially, just after interplanetary shock occurrence, a decrease in the fractal dimension for all stations is observed, not straightforwardly visible in the geomagnetic field components data.

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WANG, X., and C. B. YANG. "FRACTAL PROPERTIES OF PARTICLES IN PHASE SPACE FROM URQMD MODEL." International Journal of Modern Physics E 22, no. 04 (April 2013): 1350021. http://dx.doi.org/10.1142/s0218301313500213.

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Nonstatistical dynamical fluctuations by means of the detrended fluctuation analysis (DFA) and multifractal DFA are studied. We used a two-dimensional algorithm for the analyses. By choosing different particles generated by UrQMD code, we show that different particles all have good scaling behaviors with bin size. The correlation between different identified particles are also discussed.

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SAMADDER, SWETADRI, KOUSHIK GHOSH, and TAPASENDRA BASU. "FRACTAL ANALYSIS OF PRIME INDIAN STOCK MARKET INDICES." Fractals 21, no. 01 (March 2013): 1350003. http://dx.doi.org/10.1142/s0218348x13500035.

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The purpose of the present work is to study the fractal behaviour of prime Indian stock exchanges, namely Bombay Stock Exchange Sensitivity Index (BSE Sensex) and National Stock Exchange (NSE). To analyze the monofractality of these indices we have used Higuchi method and Katz method separately. By applying Mutifractal Detrended Fluctuation Analysis (MFDFA) technique we have calculated the generalized Hurst exponents, multifractal scaling exponents and generalized multifractal dimensions for the present indices. We have deduced Hölder exponents as well as singularity spectra for BSE and NSE. It has been observed that both the stock exchanges are possessing self-similarity at different small ranges separately and inhomogeneously. By comparing the multifractal behaviour of the BSE and NSE indices, we have found that the second one exhibits a richer multifractal feature than the first one.

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Huang, Ya-Ping, Jian-Hua Geng, and Tong-Lou Guo. "New seismic attribute: Fractal scaling exponent based on gray detrended fluctuation analysis." Applied Geophysics 12, no. 3 (September 2015): 343–52. http://dx.doi.org/10.1007/s11770-015-0509-x.

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Talebinejad, Mehran, Adrian D. C. Chan, and Ali Miri. "Fatigue estimation using a novel multi-fractal detrended fluctuation analysis-based approach." Journal of Electromyography and Kinesiology 20, no. 3 (June 2010): 433–39. http://dx.doi.org/10.1016/j.jelekin.2009.06.002.

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Popovska, Ekaterina, and Mitko Gospodinov. "Fractal Behavior in Bulgarian Day-Ahead Prices Based on Detrended Fluctuation Analysis." Innovative STEM Education 2, no. 1 (August 10, 2020): 56–64. http://dx.doi.org/10.55630/stem.2020.0207.

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This study investigates the hourly prices of the electricity day-ahead market nonstationary characteristics and long-range correlation. Using the detrended fluctuation analysis (DFA) approach, we show evidence of long memory for the Bulgarian day-ahead market between January 20th, 2016 and December 31, 2019. Furthermore, the results from the DFA methodology shows that behavior of the hourly electricity spot prices returns were long term positively correlated. DFA methods can be used as powerful tools for analyzing very volatile series like electricity prices considering the fact that in recent years prices become more volatile due to increased integration of renewables that are intermittent and far more volatile than other commodities normally considered with extreme volatility. Day ahead electricity prices are crucially important for forecasting, derivatives pricing and risk management and therefore in this paper we give a brief introduction on DFA method.

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Zehra, Sumbul, and Saif Uddin Jilani. "Comparative Analysis of Fractal Properties of Solar Faculae." International Journal of Economic and Environmental Geology 12, no. 2 (July 19, 2021): 50–59. http://dx.doi.org/10.46660/ijeeg.vol12.iss2.2021.587.

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Present study is aimed at investigating the solar faculae area from 1990 to 2007 which partially covered the22nd and 23rd solar cycle. Rescaled Range Analysis (RRA) and Detrended Fluctuation Analysis (DFA) have beenadopted to evaluate the behaviour of nonlinear dynamics of solar faculae area. Results show that the value of Hurstexponent for solar faculae area from RRA and DFA is negatively correlated. It means it is non-persistent and longrange correlated. Obtained result is inaccurate so the only solution is to transform the data into stationary data by takingdifferencing. RRA is applied on residuals and RRA to evaluate the fractal property of the time series. Solar faculae areainvestigated in this study is fractal in nature and predictable ass well. Moreover, the time series of solar faculae area isnon-linear as established by the Brock – Dechert – Scheinkman (BDS) test results

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FANCHIOTTI, H., S. J. SCIUTTO, C. A. GARCÍA CANAL, and C. HOJVAT. "ANALYSIS OF SUNSPOT NUMBER FLUCTUATIONS." Fractals 12, no. 04 (December 2004): 405–11. http://dx.doi.org/10.1142/s0218348x0400263x.

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Monthly averages of the sunspot number visible on the sun, observed from 1749, Zurich Observatory, and from 1848 other observatories, have been analyzed. This time signal presents a frequency power spectra with a clear 1/fα behavior with α≃0.8±0.2. The well-known cycle of approximately 11 years, clearly present in the spectrum, does not produce a sensible distortion of that behavior. The eventual characterization of the sunspot time series as a fractal is analyzed by means of the detrended fluctuation analysis (DFA). The jump-size distribution of the signal is also studied.

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ZHAI, MING-YUE. "ON THE BROADBAND POWER LINE COMMUNICATION SIGNALS’ DYNAMIC FEATURES." Fractals 26, no. 04 (August 2018): 1850043. http://dx.doi.org/10.1142/s0218348x18500433.

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For the purpose of transmitting data in smart grids, broadband communication over power lines (PLC) is considered to be one of the feasible technologies. Due to the multi-path effect of the signal propagation in complicate electrical networks, PLC signals present some dynamic features in time and space domains. The mono-fractal and multi-fractal theories are introduced to understand such dynamic features in PLC signals. Four common methods, namely, re-scaled range analysis, variance–time plot method, periodic diagram analysis and wavelet-based method are used to study the nonlinear properties and self-similarity. Fractal analysis at different frequencies and times is also performed to verify further. The paper also tests multi-fractal properties of PLC signals by the means of multi-fractal detrended fluctuation analysis (MFDFA). The multi-fractal spectrum of power low exponents is estimated from the measured PLC signals. We also proposed a new algorithm to improve the performance of the traditional MFDFA, where wavelet theory is integrated. By simulations, the better performance of the proposed method is verified.

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LIN, MIN, SHUANG-XI YAN, GANG ZHAO, and GANG WANG. "CORRELATIONS AND MULTIFRACTALITY IN AN EARTHQUAKE MODEL ON ASSORTATIVE SCALE-FREE NETWORKS FROM MONO- AND MULTI-FRACTAL ANALYSES." International Journal of Modern Physics C 23, no. 10 (October 2012): 1250070. http://dx.doi.org/10.1142/s0129183112500702.

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The scaling properties of the avalanches' interevent time series in a modified Olami–Feder–Christensen (OFC) earthquake model on assortative scale-free networks have been investigated. We analyze the interevent time of avalanches with size larger than or equal to S th by using rescaled range (R/S) analysis and detrended fluctuation analysis (DFA) methods. Our results demonstrate positive correlation and persistent feature of the interevent time series. The multifractal detrended fluctuation analysis (MF-DFA) has evidenced differences among the avalanches' interevents interval with different S th . We determine generalized Hurst exponent and singularity spectrum and find that the interevent time series have multifractal nature.

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HU, JING, JIANBO GAO, FRED L. POSNER, YI ZHENG, and WEN-WEN TUNG. "TARGET DETECTION WITHIN SEA CLUTTER: A COMPARATIVE STUDY BY FRACTAL SCALING ANALYSES." Fractals 14, no. 03 (September 2006): 187–204. http://dx.doi.org/10.1142/s0218348x06003210.

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Sea clutter refers to the radar returns from a patch of ocean surface. Accurate modeling of sea clutter and robust detection of low observable targets within sea clutter are important problems in remote sensing and radar signal processing applications. Due to lack of fundamental understanding of the nature of sea clutter, however, no simple and effective methods for detecting targets within sea clutter have been proposed. To help solve this important problem, we apply three types of fractal scaling analyses, fluctuation analysis (FA), detrended fluctuation analysis (DFA), and the wavelet-based fractal scaling analysis to study sea clutter. Our analyses show that sea clutter data exhibit fractal behaviors in the time scale range of about 0.01 seconds to a few seconds. The physical significance of these time scales is discussed. We emphasize that time scales characterizing fractal scaling break are among the most important features for detecting patterns using fractal theory. By systematically studying 392 sea clutter time series measured under various sea and weather conditions, we find very effective methods for detecting targets within sea clutter. Based on the data available to us, the accuracy of these methods is close to 100%.

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CHUN, WEIDE, HESEN LI, and XU WU. "PORTFOLIO MODEL UNDER FRACTAL MARKET BASED ON MEAN-DCCA." Fractals 28, no. 07 (November 2020): 2050142. http://dx.doi.org/10.1142/s0218348x2050142x.

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Under the realistic background that the capital market nowadays is a fractal market, this paper embeds the detrended cross-correlation analysis (DCCA) into the return-risk criterion to construct a Mean-DCCA portfolio model, and gives an analytical solution. Based on this, the validity of Mean-DCCA portfolio model is verified by empirical analysis. Compared to the mean-variance portfolio model, the Mean-DCCA portfolio model is more conducive for investors to build a sophisticated investment portfolio under multi-time-scale, improve the performance of portfolios, and overcome the defect that the mean-variance portfolio model has not considered the existence of fractal correlation characteristics between assets.

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FATTAHI, M. H., N. TALEBBEYDOKHTI, G. R. RAKHSHANDEHROO, A. SHAMSAI, and E. NIKOOEE. "THE ROBUST FRACTAL ANALYSIS OF TIME SERIES: CONCERNING SIGNAL CLASS AND DATA LENGTH." Fractals 19, no. 01 (March 2011): 29–49. http://dx.doi.org/10.1142/s0218348x11005099.

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In the present paper, the influence of the signal class (fBm/fGn) and the data length of time series on choosing the robust fractal analysis method have been studied. More than 1000 fBm/fGn generated time series in short, intermediate and long ranges have been analyzed using common fractal analysis methods. The chosen techniques were power spectral density, detrended fluctuation analysis, rescaled range analysis, box counting, average wavelet coefficients, and the variation method. Numerous graphs indicating the suitability of each method in terms of biases in calculating the fundamental fractal feature of time series, Hurst coefficient, were employed. The results strongly emphasized the crucial influence of the signal class as well as the data length when choosing the appropriate fractal analysis method. Furthermore, as a step forward, a study on the number of data points present in a classified class/length was performed. The effect of the number of data points could not be neglected either. Based on the results, a strategy flowchart for fractal analysis of time series has been proposed. Finally, as an empirical example, the monthly, weekly and daily scaled flow time series of Ghar-e-Aghaj River have been analyzed within the framework of the strategy flowchart.

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Zhu, Yanni, Kexin Wang, Youxin Lin, Hang Yin, Dibo Hou, Jie Yu, Pingjie Huang, and Guangxin Zhang. "An Online Contaminant Classification Method Based on MF-DCCA Using Conventional Water Quality Indicators." Processes 8, no. 2 (February 5, 2020): 178. http://dx.doi.org/10.3390/pr8020178.

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Emergent contamination warning systems are critical to ensure drinking water supply security. After detecting the existence of contaminants, identifying the types of contaminants is conducive to taking remediation measures. An online classification method for contaminants, which explored abnormal fluctuation information and the correlation between 12 water quality indicators adequately, is proposed to realize comprehensive and accurate discrimination of contaminants. Firstly, the paper utilized multi-fractal detrended fluctuation analysis (MF-DFA) to select indicators with abnormal fluctuation, used multi-fractal detrended cross-correlation analysis (MF-DCCA) to measure the cross-correlation between indicators. Subsequently, the algorithm fused the abnormal probability of each indicator and constructed the abnormal probability matrix to further judge the abnormal fluctuation of indicators using D–S evidence theory. Finally, the singularity index of the cross-correlation function and the selected indicators were used to classification by cosine distance. Experiments of five chemical contaminants at three concentration levels were implemented, and analysis results show the method can weaken disturbance of water quality background noise and other interfering factors. It effectively improved the classification accuracy at low concentrations compared with another three methods, including methods using triple standard deviation threshold and single indicator fluctuation analysis-only methods without fluctuation analysis. This can be applied to water quality emergency monitoring systems to reduce contaminant misclassification.

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Gospodinova, Evgeniya, Penio Lebamovski, Galya Georgieva-Tsaneva, Galina Bogdanova, and Diana Dimitrova. "Methods for Mathematical Analysis of Simulated and Real Fractal Processes with Application in Cardiology." Mathematics 10, no. 19 (September 21, 2022): 3427. http://dx.doi.org/10.3390/math10193427.

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In the article, a comparative analysis is performed regarding the accuracy parameter in determining the degree of self-similarity of fractal processes between the following methods: Variance-Time plot, Rescaled Range (R/S), Wavelet-based, Detrended Fluctuation Analysis (DFA) and Multifractal Detrended Fluctuation Analysis (MFDFA). To evaluate the methods, fractal processes based of Fractional Gaussian Noise were simulated and the dependence between the length of the simulated process and the degree of self-similarity was investigated by calculating the Hurst exponent (H > 0.5). It was found that the Wavelet-based, DFA and MFDFA methods, with a process length greater than 214 points, have a relative error of the Hurst exponent is less than 1%. A methodology for the Wavelet-based method related to determining the size of the scale and the wavelet algorithm was proposed, and it was investigated in terms of the exact determination of the Hurst exponent of two algorithms: Haar and Daubechies with different number of coefficients and different values of the scale. Based on the analysis, it was determined that the Daubechies algorithm with 10 coefficients and scale (i = 2, j = 10) has a relative error of less than 0.5%. The three most accurate methods are applied to the study of real cardiac signals of two groups of people: healthy and unhealthy (arrhythmia) subjects. The results of the statistical analysis, using the t-test, show that the proposed methods can distinguish the two studied groups and can be used for diagnostic purposes.

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Xie, Xuebin, Shaoqian Li, and Jiang Guo. "Study on Multiple Fractal Analysis and Response Characteristics of Acoustic Emission Signals from Goaf Rock Bodies." Sensors 22, no. 7 (April 2, 2022): 2746. http://dx.doi.org/10.3390/s22072746.

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Based on the actual monitoring data of the acoustic emission (AE) ground pressure monitoring and positioning system, this paper introduces fractal theory and the multifractal detrended fluctuation analysis (MF-DFA) method to estimate the waveform multifractal spectrum of goaf rock acoustic emission signals and investigate multifractal time-varying response characteristics. The research results show that the wavelet hard thresholding method has the best noise reduction effect on the original signal, and the box counting dimension has a strong waveform identification effect. Before deformation damage occurs, fractal spectral width Δα shows an increase and then decrease and the fluctuation scale factor Δf(α) decreases and then increases. When damage occurs, fractal spectral width Δα decreases and then stabilizes and concentrates. Simultaneously, the fluctuation scale factor Δf(α) keeps decreasing until the lowest point, and then shows an increasing trend until it reaches a stable state. This study is of great significance to the stability evaluation and disaster early warning of mine goaf.

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KNEŽEVIĆ, ANDREA, and MLADEN MARTINIS. "(MULTI)FRACTALITY OF PHYSIOLOGICAL TIME-SERIES." International Journal of Bifurcation and Chaos 16, no. 07 (July 2006): 2103–10. http://dx.doi.org/10.1142/s0218127406015945.

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This paper contains the application of fractal concept in analyzing heartbeat (RR interval) fluctuations measured under controlled physical activity for subjects with stable angina pectoris (SAP). Results that illustrate the separation ability of the nonlinear methods, such as the Hurst R/S method, the detrended fluctuation analysis, DFA, and the method of G-moments, in distinguishing healthy from SAP subjects in scaling parameter space are presented.

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Yonaiguchi, N., Y. Ida, M. Hayakawa, and S. Masuda. "A comparison of different fractal analyses for VHF electromagnetic emissions and their self-organization for the off-sea Miyagi-prefecture earthquake." Natural Hazards and Earth System Sciences 7, no. 4 (August 24, 2007): 485–93. http://dx.doi.org/10.5194/nhess-7-485-2007.

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Abstract. The VHF electromagnetic noise intensity data at several stations in the Tohoku area of Japan during the period of a rather large (with magnitude of 7.2) earthquake (Miyagi-ken oki earthquake) taken place on 16 August 2005, are analyzed by means of different fractal analysis methods, including (1) spectral slope estimation, (2) multi-fractal detrended fluctuation analysis and (3) multi-fractal wavelet transform modulus maxima method. It seems to the authors that there is no definite analysis method for the analysis of any seismogenic phenomenon, so that the only way we have to take, is to apply different methods to the same data for the detailed comparison of the results. This comparison enables us to deduce the properties commonly observed by the above methods. Because the most important feature common to these three methods, is that significant changes in fractal scaling characteristics are observed just during the earthquake (mainly before the earthquake) only at one station of Kunimi. Finally, we can come to the definite conclusion on the self-organization of VHF emissions only at one station in the present case.

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LAHMIRI, SALIM. "A LOOK AT SHORT- AND LONG-TERM NONLINEAR DYNAMICS IN FAMILY BUSINESS STOCK RETURNS LISTED ON CASABLANCA STOCK EXCHANGE." Fractals 27, no. 08 (November 8, 2019): 1950140. http://dx.doi.org/10.1142/s0218348x19501408.

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Moroccan family business companies are becoming an attractive investment in Casablanca stock exchange. In this study, presence of fractal and chaos in Moroccan family business stock returns is examined. In particular, return series are analyzed by stationary wavelet transform to decompose original series into long- and short-term variations. Then, detrended fluctuation analysis and artificial neural networks are used to estimate, respectively Hurst exponent and largest Lyapunov exponent. Results from fractal analysis show that short variations in returns are anti-persistent, whilst long variations are persistent. Besides, results from chaos tests reveal that both short and long variations in returns are chaotic. Such conclusions should be taken into account in active portfolio optimization and management.

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Xu, Chao, Jinchuan Ke, Zhikai Peng, Wen Fang, and Yu Duan. "Asymmetric Fractal Characteristics and Market Efficiency Analysis of Style Stock Indices." Entropy 24, no. 7 (July 13, 2022): 969. http://dx.doi.org/10.3390/e24070969.

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As a typical complex system, the stock market has attracted the attention of scholars and investors to comprehensively understand its fractal characteristics and analyze its market efficiency. Firstly, this paper proposes an asymmetric, detrended fluctuation analysis based on overlapping sliding windows (OSW-A-MFDFA). It reduces the generation of fluctuation errors, and the calculation results are more robust and reliable. The advantage of the OSW-A-MFDFA is that it not only can reveal the multifractal characteristics of time series clearly, but also can further accurately analyze the asymmetry of fractal characteristics under different trends. Secondly, this paper focuses on the variation in the width difference and height difference of the multifractal spectrum under different trends. Finally, based on multifractality, this paper proposes a comprehensive indicator MED that can be used to measure market efficiency, which is characterized by traversing all fluctuation orders. The application revealed many interesting findings in style stock indices. Style stock indices have asymmetric multifractal characteristics, and there are significant differences in the fractal spectrum of different style assets. Moreover, the market efficiency of style stock indices is time-varying, which can be reasonably explained from the perspective of the adaptive market hypothesis.

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Xiong Jie, Chen Shao-Kuan, Wei Wei, Liu Shuang, and Guan Wei. "Multi-fractal detrended fluctuation analysis algorithm based identification method of scale-less range for multi-fractal charateristics of traffic flow." Acta Physica Sinica 63, no. 20 (2014): 200504. http://dx.doi.org/10.7498/aps.63.200504.

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Roume, Clément, Samar Ezzina, Hubert Blain, and Didier Delignières. "Biases in the Simulation and Analysis of Fractal Processes." Computational and Mathematical Methods in Medicine 2019 (December 3, 2019): 1–12. http://dx.doi.org/10.1155/2019/4025305.

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Fractal processes have recently received a growing interest, especially in the domain of rehabilitation. More precisely, the evolution of fractality with aging and disease, suggesting a loss of complexity, has inspired a number of studies that tried, for example, to entrain patients with fractal rhythms. This kind of study requires relevant methods for generating fractal signals and for assessing the fractality of the series produced by participants. In the present work, we engaged a cross validation of three methods of generation and three methods of analysis. We generated exact fractal series with the Davies–Harte (DH) algorithm, the spectral synthesis method (SSM), and the ARFIMA simulation method. The series were analyzed by detrended fluctuation analysis (DFA), power spectral density (PSD) method, and ARFIMA modeling. Results show that some methods of generation present systematic biases: DH presented a strong bias toward white noise in fBm series close to the 1/f boundary and SSM produced series with a larger variability around the expected exponent, as compared with other methods. In contrast, ARFIMA simulations provided quite accurate series, without major bias. Concerning the methods of analysis, DFA tended to systematically underestimate fBm series. In contrast, PSD yielded overestimates for fBm series. With DFA, the variability of estimates tended to increase for fGn series as they approached the 1/f boundary and reached unacceptable levels for fBm series. The highest levels of variability were produced by PSD. Finally, ARFIMA methods generated the best series and provided the most accurate and less variable estimates.

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Wang, Xuefei, Yichao Zhou, and Chunxia Zhao. "Heart-rate analysis of healthy and insomnia groups with detrended fractal dimension feature in edge." Tsinghua Science and Technology 27, no. 2 (April 2022): 325–32. http://dx.doi.org/10.26599/tst.2021.9010030.

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Liu, Hongmei, Jichang Zhang, Yujie Cheng, and Chen Lu. "Fault diagnosis of gearbox using empirical mode decomposition and multi-fractal detrended cross-correlation analysis." Journal of Sound and Vibration 385 (December 2016): 350–71. http://dx.doi.org/10.1016/j.jsv.2016.09.005.

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TELESCA, LUCIANO, GERARDO COLANGELO, VINCENZO LAPENNA, JENS HEINICKE, and ULRICH KOCH. "QUANTITATIVE DYNAMICS IN GEOPHYSICAL PARAMETERS SIMULTANEOUSLY RECORDED IN THE SOOS NATURE PARK (CZECH REPUBLIC)." Fluctuation and Noise Letters 03, no. 01 (March 2003): L73—L82. http://dx.doi.org/10.1142/s0219477503001105.

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Time dynamics of self-potential, geochemical and meteorological parameters, simultaneously recorded in a CO 2 degassing area at Soos, NW-Bohemia (Czech Republic), have been investigated. The power spectra, behaving as power-law function of the frequency, show the presence of colored-noise-type dynamics. The Higuchi analysis reveals the observed geophysical signals to have the property of fractal curves, with the identification of different scaling regimes. The Detrended Fluctuation Analysis, removing trends and non-stationarities, has shown that the signals present clear fingerprints of long-range correlated fluctuations.

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Agbazo, Medard Noukpo, Gabin Koto N’Gobi, Eric Alamou, Basile Kounouhewa, and Abel Afouda. "Fractal Analysis of the Long-Term Memory in Precipitation over Bénin (West Africa)." Advances in Meteorology 2019 (January 9, 2019): 1–12. http://dx.doi.org/10.1155/2019/1353195.

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This study analyzed the long-term memory (LTM) in precipitation over Bénin synoptic stations from 1951 to 2010 using the detrended fluctuation analysis (DFA) method. Results reveal the existence of positive long-term memory characteristic in rainfall field. DFA exponent values are different regarding the concerned synoptic stations, reflecting the effect of geographical position and climate on the LTM. These values were related to the type of climate. The best DFA1-4 method depends on the geographical position of the studied station. However, DFA2 is generally the best in terms of spatial average from DFA1 to DFA4. In Bénin synoptic stations, except the Parakou station, the long-term temporal correlations are systematically the source of multifractality in rainfall. Except Natitingou, the strength of long-term memory characteristic decreases each twenty years in the study period. Considering the fractal approach, our results show that the subperiod 1991–2010 is not really a transition period as shown before. Thus, the drought is prolonging until 2010. So, fractal theory reveals more Bénin climatic characteristics.

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DENG, WEIBING, WEI LI, and XU CAI. "NONLINEAR PROPERTIES, FRACTAL BEHAVIOR AND LONG-RANGE CORRELATION ANALYSIS OF THE CHINESE FUND MARKET." International Journal of Modern Physics C 21, no. 01 (January 2010): 79–95. http://dx.doi.org/10.1142/s0129183110014963.

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Applying the statistical hypothesis testing, we investigate several nonlinear properties embedded in the return series of the Chinese Fund Market (CFM), which suggests the series is non-normal, auto-correlative and heteroskedastic. We hereby analyze the Hurst exponent of the return series in different timescales on the basis of the detrended fluctuation analysis (DFA) algorithm, and discuss the fractal behavior of the CFM. Furthermore, by studying the correlation of different weights in the volatility, we find the persistent long-range power-law correlation exists in the time series. We also provide hints that the above statistical properties are insensitive to the funds kind, and may be irrelevant to the market phases. Our work may reveal the self-similarity characteristics of the financial market and show a better understanding of the CFM.

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De Santis, Enrico, Parisa Naraei, Alessio Martino, Alireza Sadeghian, and Antonello Rizzi. "Multifractal Characterization and Modeling of Blood Pressure Signals." Algorithms 15, no. 8 (July 26, 2022): 259. http://dx.doi.org/10.3390/a15080259.

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In this paper, a multi-fractal analysis on a diastolic blood pressure signal is conducted. The signal is measured in a time span of circa one day through the multifractal detrended fluctuation analysis framework. The analysis is performed on asymptotic timescales where complex regulating mechanisms play a fundamental role in the blood pressure stability. Given a suitable frequency range and after removing non-stationarities, the blood pressure signal shows interesting scaling properties and a pronounced multifractality imputed to long-range correlations. Finally, a binomial multiplicative model is investigated showing how the analyzed signal can be described by a concise multifractal model with only two parameters.

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Ma, Yiran, Xinyi He, Rui Wu, and Chenhua Shen. "Spatial Distribution of Multi-Fractal Scaling Behaviours of Atmospheric XCO2 Concentration Time Series during 2010–2018 over China." Entropy 24, no. 6 (June 11, 2022): 817. http://dx.doi.org/10.3390/e24060817.

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Exploring the spatial distribution of the multi-fractal scaling behaviours in atmospheric CO2 concentration time series is useful for understanding the dynamic mechanisms of carbon emission and absorption. In this work, we utilise a well-established multi-fractal detrended fluctuation analysis to examine the multi-fractal scaling behaviour of a column-averaged dry-air mole fraction of carbon dioxide (XCO2) concentration time series over China, and portray the spatial distribution of the multi-fractal scaling behaviour. As XCO2 data values from the Greenhouse Gases Observing Satellite (GOSAT) are insufficient, a spatio-temporal thin plate spline interpolation method is applied. The results show that XCO2 concentration records over almost all of China exhibit a multi-fractal nature. Two types of multi-fractal sources are detected. One is long-range correlations, and the other is both long-range correlations and a broad probability density function; these are mainly distributed in southern and northern China, respectively. The atmospheric temperature and carbon emission/absorption are two possible external factors influencing the multi-fractality of the atmospheric XCO2 concentration. Highlight: (1) An XCO2 concentration interpolation is conducted using a spatio-temporal thin plate spline method. (2) The spatial distribution of the multi-fractality of XCO2 concentration over China is shown. (3) Multi-fractal sources and two external factors affecting multi-fractality are analysed.

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Tilfani, Oussama, and My Youssef El Boukfaoui. "Multifractal Analysis of African Stock Markets During the 2007–2008 US Crisis." Review of Pacific Basin Financial Markets and Policies 22, no. 04 (December 2019): 1950022. http://dx.doi.org/10.1142/s021909151950022x.

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In this paper, we examine the effects of subprime crisis on the largest African stock markets (South Africa, Nigeria, Egypt, and Morocco) by testing the fractal market hypothesis. We use a rolling window Multifractal Detrended Fluctuation Analysis, and find decline in local Hurst exponent and an increase in short-term trading activity for all considered stock markets during the global financial crisis. We furthermore investigate the interrelationships of African and the American stock markets using multi-scale contagion test. Findings suggest that the cross-correlation of African stock markets increases with American markets becoming higher during the crisis sub-period. However, the presence of contagion or interdependence effects are country and time horizon-dependent. Implications of the results are discussed.

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GÁLVEZ-COYT, G., A. MUÑOZ-DIOSDADO, J. L. DEL RÍO-CORREA, and F. ANGULO-BROWN. "A COMPARATIVE STUDY OF VALIDITY RANGES OF SOME FRACTAL METHODS OF TIME SERIES ANALYSIS." Fractals 18, no. 02 (June 2010): 235–46. http://dx.doi.org/10.1142/s0218348x10004774.

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Each fractal method of time series analysis gives origin to a parameter that characterizes them. For example, β is the resulting parameter of the application of spectral analysis, α for detrended fluctuation analysis (DFA), D for Higuchi's method and Ha for semivariogram, to mention only some of them. Diverse linear relations between the mentioned parameters have been reported; some of these relations have been obtained from theoretical approaches by assuming time series properties such as their self-similarity. The obtained relations are linear in all cases; nevertheless, these relations only have a limited validity range. In this work, we determine the relation between each one of the parameters ß, α and D for a suitable value range. This is done by means of numerical experiments, consisting of the generation of self-affine and fractal synthetic series. Each one of these sets has a minimum of 500 series with pre-established values of ß, D and Ha. In addition, these are constructed in a suitable value range for each generation method. Later, we apply fractal methods to each one of the three sets of series and the relations between the parameters are obtained. It is observed that all the relations have a linear part as it is expected, but there exist differences in the validity range depending on the generation method.

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Wang, Xianxun, Yadong Mei, Weinan Li, Yanjun Kong, and Xiangyu Cong. "Influence of Sub-Daily Variation on Multi-Fractal Detrended Fluctuation Analysis of Wind Speed Time Series." PLOS ONE 11, no. 1 (January 7, 2016): e0146284. http://dx.doi.org/10.1371/journal.pone.0146284.

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Yeh, Chien-Hung, Chung-Hau Juan, Huei-Ming Yeh, Cheng-Yen Wang, Hsu-Wen Vincent Young, Jiunn-Lee Lin, Chen Lin, Lian-Yu Lin, and Men-Tzung Lo. "The critical role of respiratory sinus arrhythmia on temporal cardiac dynamics." Journal of Applied Physiology 127, no. 6 (December 1, 2019): 1733–41. http://dx.doi.org/10.1152/japplphysiol.00262.2019.

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Temporal cardiac properties provide alternative information in analyzing heart rate variability (HRV), which may be disregarded by the standard HRV analyses. Patients with congestive heart failure (CHF) are known to have distinct temporal features from the healthy individuals. However, the underlying mechanism leading to the variation remains unclear. Whether or not these parameters can finely classify the severity for CHF patients is uncertain as well. In this work, an electrocardiogram was monitored in advanced CHF patients using 24-h Holter in four conditions, including baseline, one and three months after atenolol therapy, and healthy individuals. Slope and area under the curve (AUC) of multiscale entropy (MSE) curve over short (scales 1–5) and long (scales 6–20) scales, and detrended fluctuation analysis (DFA) scaling exponents at short (4–11 beats) and intermediate (>11 beats) window sizes were calculated. The results show that short-time scale MSE-derived parameters (slope: −0.08 ± 0.10, −0.03 ± 0.10, 0.02 ± 0.06, 0.08 ± 0.06; AUC: 4.03 ± 2.11, 4.69 ± 1.28, 4.73 ± 0.94, and 6.17 ± 1.23) and short-time scale DFA exponent (0.79 ± 0.16, 0.95 ± 0.22, 1.11 ± 0.19, and 1.35 ± 0.20) can hierarchically classify all four conditions. More importantly, simulated R-R intervals with different fractions and amplitude of respiratory sinus arrhythmia (RSA) components were examined to validate our hypothesis regarding the essentiality of RSA in the improvement of cardiovascular function, and its tight association with unpredictability and fractal property of HRV, which is in line with our hypothesis that RSA contributes significantly to the generation of the unpredictability and fractal behavior of HR dynamics. NEW & NOTEWORTHY Temporal cardiac properties provide useful diagnostic parameters for patients with congestive heart failure (CHF). Our study hierarchically classified CHF patients with β-blocker treatment by using multiscale entropy and detrended fluctuation analysis. Also, we provided the evidence to validate the critical role of respiratory sinus arrhythmia in the fractal properties of heart rate variability.

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Heffernan, Kevin S., Jacob J. Sosnoff, Christopher A. Fahs, Kevin K. Shinsako, Sae Young Jae, and Bo Fernhall. "Fractal scaling properties of heart rate dynamics following resistance exercise training." Journal of Applied Physiology 105, no. 1 (July 2008): 109–13. http://dx.doi.org/10.1152/japplphysiol.00150.2008.

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With aging and disease, there is a breakdown of the natural fractal-like organization of heart rate (HR). Fractal-like correlation properties of HR can be assessed with detrended fluctuation analysis (DFA). A short-time scaling exponent (αs) value of 1 is associated with healthy HR dynamics, whereas values that deviate away from 1, in either direction, indicate fractal collapse. The purpose of this study was to examine the effect of resistance exercise training (RT) on fractal correlation properties of HR dynamics. Resting ECG was collected at baseline, following a 4-wk time control period and 6 wk of RT (3 days per wk) in 34 men (23 ± 1 years of age). Fractal properties of HR were assessed with DFA. There was no change in αs following either the time control period or RT (1.01 ± 0.06 to 0.98 ± 0.06 to 0.93 ± 0.04, P > 0.05). Given the potential bidirectional nature of fractal collapse, subjects were retrospectively separated into two groups (higher αs and lower αs) on the basis of the initial αs by using cluster analysis. An interaction was detected for αs following RT ( P < 0.05). There was no change in αs in either group following the time control, but αs increased following RT in the lower αs group ( n = 18; 0.73 ± 0.04 to 0.69 ± 0.04 to 0.88 ± 0.04) and αs decreased following RT in the higher αs group ( n = 16; 1.20 ± 0.04 to 1.24 ± 0.04 to 0.98 ± 0.04). In conclusion, RT improves fractal properties of HR dynamics.

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Journal articles on the topic 'Detrended fractal analysis'

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