×

Multi-affine visible height correlation analysis for revealing rich structures of fractal time series. (English) Zbl 1498.62171


MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
Full Text: DOI

References:

[1] Kantelhardt, J. W.; Koscielny-Bunde, E.; Rego, H. A.H., Detecting long range correlations with detrended fluctuation analysis, Phys A, 295, 441-454 (2001) · Zbl 0978.37057
[2] Kantelhardt, J. W., Fractal and multifractal time series, Mathematics of complexity and dynamical systems, 463-487 (2012), Springer: Springer New York
[3] Hunt, G. A., Random Fourier transforms, Trans Am Math Soc, 71, 1, 38-69 (1951) · Zbl 0043.30601
[4] Hurst, H. E., Methods of using long-term storage in reservoirs, Proc Inst Civ Eng, 5, 5, 519-543 (1956)
[5] Peng, C. K.; Buldyrev, S. V., Long-range correlations in nucleotide sequences, Nature, 356, 6365, 168-170 (1992)
[6] Cohen, A.; Daubechies, I.; Feauveau, J. C., Biorthogonal bases of compactly supported wavelets, Commun Pure Appl Math, 45, 5, 485-560 (1992) · Zbl 0776.42020
[7] Kantelhardt, J. W.; Roman, H. E.; Greiner, M., Discrete wavelet approach to multifractality, Phys A, 220, 3-4, 219-238 (1995)
[8] Muzy, J. F.; Bacry, E.; Arneodo, A., Wavelets and multifractal formalism for singular signals: application to turbulence data, Phys Rev Lett, 67, 3515 (1991)
[9] Peng, C. K.; Buldyrev, S. V.; Havlin, S., Mosaic organization of DNA nucleotides, Phys Rev E, 49, 2, 1685 (1994)
[10] Alessio, E.; Carbone, A.; Castelli, G., Second-order moving average and scaling of stochastic time series, Eur Phys J B, 27, 2, 197-200 (2002)
[11] Kantelhardt, J. W.; Zschiegner, S. A.; Koscienlny-Bunde, E., Multifractal detrended fluctuation analysis of nonstationary time series, Phys A, 316, 1-4, 87-114 (2002) · Zbl 1001.62029
[12] Gu, G. F.; Zhou, W. X., Detrending moving average algorithm for multifractals, Phys Rev E, 82, 011136 (2010)
[13] Barabási, A. L.; Szźpfalusy, P.; Vicsek, T., Multifractal spectra of multi-affine functions, Phys A, 178, 1, 17-28 (1991)
[14] Barabási, A. L.; Vicsek, T., Multifractality of self-affine fractals, Phys Rev A, 44, 4, 2730 (1991)
[15] Kristoufek, L., Multifractal height cross-correlation analysis: a new method for analyzing long-range cross-correlations, Europhys Lett, 95, 6, 68001 (2011)
[16] Wang, F.; Yang, Z. H.; Wang, L., Detecting and quantifying cross-correlations by analogous multifractal height cross-correlation analysis, Phys A, 444, 954-962 (2016)
[17] Wang, F.; Wang, L.; Chen, Y., Quantifying the range of cross-correlated fluctuations using a \(q - l\) dependent AHXA coefficient, Phys A, 494, 454-464 (2018)
[18] Wang, F.; Wang, L.; Chen, Y. M., Lagged multi-affine height correlation analysis for exploring lagged correlations in complex systems, Chaos, 28, 6, 061102 (2018)
[19] Hosseinabadi, S.; Masoudi, A. A., Random deposition with spatially correlated noise (RD-SCN) model: multi-affine analysis, Chaos, Solitons Fractals, 143, 110596 (2021) · Zbl 1498.82015
[20] Yang, J. Y.; Yu, Z. G.; Anh, V., Clustering structures of large proteins using multifractal analyses based on a 6-letter model and hydrophobicity scale of amino acids, Chaos, Solitons Fractals, 40, 2, 607-620 (2009)
[21] Gieraltowski, J.; Zebrowski, J.; Baranowski, R., Multiscale multifractal analysis of heart rate variability recordings with a large number of occurrences of arrhythmia, Phys Rev E, 85, 021915 (2012)
[22] Fan, Q. J.; Liu, S. G.; Wang, K. H., Multiscale multifractal detrended fluctuation analysis of multivariate time series, Phys A, 532, 121864 (2019)
[23] 1689 · Zbl 1478.62251
[24] Wang, F.; Fan, Q. J.; Stanley, H. E., Multiscale multifractal detrended-fluctuation analysis of two- dimensional surfaces, Phys Rev E, 93, 4, 042213 (2016)
[25] Ge, X. L.; Lin, A. J., Multiscale multifractal detrended partial cross-correlation analysis of chinese and american stock markets, Chaos, Solitons Fractals, 145, 110731 (2021)
[26] De Berg, M.; Kreveld, M. V.; Overmars, M., Computational geometry, Computational geometry, 1-17 (2000), Springer, Berlin Heidelberg · Zbl 0939.68134
[27] Lacasa, L.; Luque, B.; Ballesteros, F., From time series to complex networks: the visibility graph, Proc Natl Acad Sci, 105, 13, 4972-4975 (2008) · Zbl 1205.05162
[28] Luque, B.; Lacasa, L.; Ballesteros, F., Horizontal visibility graphs: exact results for random time series, Phys Rev E, 80, 4, 046103 (2009)
[29] Panwar, H.; Gupta, P. K.; Siddiqui, M. K., A deep learning and grad-CAM based color visualization approach for fast detection of COVID-19 cases using chest x-ray and CT-scan images, Chaos, Solitons Fractals, 140, 110190 (2020)
[30] Gao, Z. K.; Cai, Q.; Yang, Y. X., Visibility graph from adaptive optimal kernel time-frequency representation for classification of epileptiform EEG, Int J Neural Syst, 27, 04, 1750005 (2017)
[31] Zhao, X.; Sun, J.; Zhang, N., Extreme events analysis of non-stationary time series by using horizontal visibility graph, Fractals, 28, 05, 2050089 (2020)
[32] Xu, P.; Zhang, R.; Deng, Y., A novel visibility graph transformation of time series into weighted networks, Chaos, Solitons Fractals, 117, 201-208 (2018) · Zbl 1443.90145
[33] Li, S.; Shang, P., Analysis of nonlinear time series using discrete generalized past entropy based on amplitude difference distribution of horizontal visibility graph, Chaos, Solitons Fractals, 144, 110687 (2021)
[34] Zheng, M.; Domanskyi, S.; Piermarocchi, C., Visibility graph based temporal community detectiolicatn with appions in biological time series, Sci Rep, 11, 1, 1-12 (2021)
[35] Manshour, P., Complex network approach to fractional time series, Chaos, 25, 10, 103105 (2015) · Zbl 1378.62078
[36] Zhang, R.; Zou, Y.; Zhou, J., Visibility graph analysis for re-sampled time series from auto-regressive stochastic processes, Commun Nonlinear Sci Numer Simul, 42, 396-403 (2017) · Zbl 1473.62323
[37] Zou, Y.; Small, M.; Liu, Z., Complex network approach to characterize the statistical features of the sunspot series, New J Phys, 16, 1, 013051 (2014)
[38] Zou, Y.; Donner, R. V.; Marwan, N., Complex network approaches to nonlinear time series analysis, Phys Rep, 787, 1-97 (2019)
[39] Hosking, J. R., Fractional differencing, Biometrika, 68, 1, 165-176 (1981) · Zbl 0464.62088
[40] Rosso, O.; Larrondo, H.; Martin, M., Distinguishing noise from chaos, PhysRev Lett, 99, 154102 (2007)
[41] Li, Q.; Fu, Z.; Yuan, N., Beyond Benford’s law: distinguishing noise from chaos, PLoS One, 10, 6, E0129161 (2015)
[42] Grassberger, P.; Procaccia, I., Measuring the strangeness of strange attractors, Phys D, 9, 1-2, 189-208 (1983) · Zbl 0593.58024
[43] Hénon, M., A two-dimensional mapping with a strange attractor, Commun Math Phys, 50, 1, 69-77 (1976) · Zbl 0576.58018
[44] Lorenz, E. N., Deterministic nonperiodic flow, J Atmos Sci, 20, 2, 130-141 (1963) · Zbl 1417.37129
[45] Prichard, D.; Theiler, J., Generating surrogate data for time series with several simultaneously measured variables, Phys Rev Lett, 73, 7, 951 (1994)
[46] Kostelich, E. J.; Schreiber, T., Noise reduction in chaotic time-series data: a survey of common methods, Phys Rev E, 48, 3, 1752 (1993)
[47] Chan, G.; Wood, A. T.A., Simulation of multifractional Brownian motion, COMPSTAT, 233-238 (1998), Phys, Heidelberg · Zbl 0952.65006
[48] Shao, Y.; Gu, G.; Jiang, Z., Comparing the performance of FA, DFA and DMA using different synthetic long-range correlated time series, Sci Rep, 2, 1, 1-5 (2012)
[49] Pessa, A. A.B.; Ribeiro, H. V., Characterizing stochastic time series with ordinal networks, Phys Rev E, 100, 4, 042304 (2019)
[50] Wang, F.; Liao, G. P.; Zhou, X. Y., Multifractal detrended cross-correlation analysis for power markets, Nonlinear Dyn, 72, 1-2, 353-363 (2013)
[51] Wang, F.; Liao, G. P.; Li, J. H., Cross-correlation detection and analysis for California’s electricity market based on analogous multifractal analysis, Chaos, 23, 1, 013129 (2013)
[52] Wang, F., A novel coefficient for detecting and quantifying asymmetry of California electricity market based on asymmetric detrended cross-correlation analysis, Chaos, 26, 6, 063109 (2016)
[53] Wang, F.; Fan, Q. J.; Wang, K. H., Asymmetric multiscale multifractal detrended cross-correlation analysis for the 1999-2000 California electricity market, Nonlinear Dyn, 91, 3, 1527-1540 (2018)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.