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Time Series Analysis Using Fractal and Multifractal Methods

Published: 21 June 2019 Publication History

Abstract

The article presents a theoretical development of the application of mathematical methods for fractal and multifractal analysis in the study of non-linear, non-stationary time series. The research was conducted using Detrended Fluctuation Analysis (DFA) and MultiFractal Detrended Fluctuation Analysis (MFDFA). A characteristic feature of the application of these methods is that they allow for additional information to be obtained from the studied objects, providing an insight into the objects' nonlinear dynamic nature. In the present case, the subjects of the analyses are fluctuations in the physiological signals of the heartbeat. The data is obtained through specialized electronic devices (holters) that record intervals during a 24-hour heart rate registration period. The dynamic characteristics of the heart rate intervals, converted by electronic devices into a time series, show fractal and in some cases multifractal properties. Conducting studies on prolonged time series, which reflect the functioning of cardiac activity in both healthy subjects and those with cardiovascular changes, has made it possible to assess with a high level of confidence the degree of the disease or lack thereof. A suitable approach for these studies is the use of modern mathematical methods for fractal and multifractal analysis of the heart rate signals.

References

[1]
M.D. Costa, R.B. Davis, A.L.Goldberger (2017). Heart Rate Fragmentation: A New Approach to the Analysis or Cardiac Interbeat Internal Dynamics. Front. Physiol, 8:255.
[2]
J.W. Kantelhardt (2008). Fractal and Multifractal Time Series. Physics.data-an, 1--59.
[3]
C.-K. Peng, S.V. Buldyrev, S. Havlin, M. Simons, H.E. Stanley and A.L. Goldberger (1994). Mosaic Organization of DNA nucleotides. Physical Review E, 49(2), 1685--1689.
[4]
C.-K. Peng, S. Havlin, H.E. Stanley and A.L. Goldberger (1995). Quantification of Scaling Exponents and Crossover Phenomena in Nonstationary Heartbeat Time Series. CHAOS 5(1), 82--87.
[5]
A.K. Golińska (2012). Detrended Fluctuation Analysis (DFA) in Biomedical Signal Processing: Selected Examples. Studies in Logic, Grammar and Rhetoric, 29(42), 107--115.
[6]
D. Maraun, H.W. Rust, J. Timmer (2004). Tempting long-memory - on the interpretation of DFA results. Nonlinear Processes in Geophysics, European Geosciences Union (EGU), 11(4), 495--503.
[7]
U.R. Acharya, J.S. Suri, J.A.E. Spaan, S.M. Krishnan, 2007, Advances in Cardiac Signal Processing. Springer-Verlag Berlin Heidelberg.
[8]
G. Ernst, 2014, Heart Rate Variability. Springer-Verlag London.
[9]
O.I. Sheluhin, S.M. Smolskiy, A.V. Osin, 2007, Self-Similar Processes in Telecommunications, John Wiley & Sons, Ltd, England.
[10]
J.W. Kantelhardt, S.A. Zschiegner, E. Koscielny-Bunde, S. Havlin, A. Bunde, H.E. Stanley (2002). Multifractal detrended fluctuation analysis of nonstationary time series. Physica A: Statistical Mechanics and its Applications, 316(1-4), 87--114.
[11]
A. Biswas, T.B. Zeleke, and B.C. Si (2012). Multifractal detrended fluctuation analysis in examining scaling properties of the spatial patterns of soil water storage. Nonlinear Processes in Geophysics, 19, 227--238.
[12]
E. Li, X. Mu, G. Zhao, P. Gao (2015). Multifractal Detrended Fluctuation Analysis of Streamflow in the Yellow River Bain, China. Water 7(4),1670-1686.
[13]
B. Mandelbrot, 1997, Fractals and Scaling in Finance. New York: Springer.
[14]
M.V. Kamath, M.A. Watanabe, A.R.M. Upton (Ed.), 2016, Heart Rate Variability (HRV) Signal Analysis: Clinical Applications, CRC Press Taylor&Francis Group.
[15]
T. Kalisky, Y. Ashkenazy and S. Havlin (2007). Volatility of fractal and multifractal time series. Israel Journal of Earth Sciences, 65, 47--56.
[16]
R. Mulligan (2004). Fractal analysis of highly volatile markets: an application to technology equities. The Quarterly Review of Economics and Finance, 44(1), 155--179.
[17]
M. Kale, F.B. Butar (2011). Fractal analysis of Time Series and Distribution Properties of Hurst Exponent. Journal of Mathematical Sciences&Mathematics Education, 5(1), 8--19.
[18]
D. Makowiec (2009). Multifractal estimates of monofractality in RR-heart series in power spectrum ranges. Physica A: Statistical Mechanics and its Applications, 388(17), 3486--3502.
[19]
Z. Yu, L. Yee,Y. Zu-Guo (2011). Relationships of exponents in multifractal detrended fluctuation analysis and convential multifractal analysis. Chin. Phys. B, 20(9), 090507_1-090507_9.
[20]
E. Gospodinova, M. Gospodinov, N. Dey, I. Domuschiev, A. Ashour, S. Balas, T. Olariu (2016). Specialized Software System for Heart Rate Variability Analysis: An Implementation of Nonlinear Graphical Methods. Soft Computing Applications, Advances in Intelligent Systems and Computing, 633, 367--374.
[21]
M. Malik (1996). Heart Rate Variability: Standards of Measurement, Physiological Interpretation, and Clinical Use: Task Force of the European Society of Cardiology and the North American Society for Pacing and Electrophysiology, Annals of Noninvasive Electrocardiology, 1, 151--181.
[22]
G. Georgieva-Tsaneva (2018). Heart Rate Variability Generating based on Mathematical Tools, Proceedings of 19th International Conference on Computer Systems and Technologies-CompSysTech'18, (Eds. B. Rachev, A. Smrikarov), ACM New York, NY, USA, ISSN 1314-9687, pp. 134--138.
[23]
G. Georgieva-Tsaneva (2019). Effective information methods for description and storage of data in health care. International Journal of Mechanical Engineering and Technology, Vol. 10 (2), 2019, pp. 708--715.

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  • (2021)Fractal Analysis and Interpretation of Temporal Patterns of TSP and PM10 Mass Concentration over Tarkwa, GhanaEarth Systems and Environment10.1007/s41748-021-00237-25:3(635-654)Online publication date: 25-Jun-2021

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  1. Time Series Analysis Using Fractal and Multifractal Methods

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        cover image ACM Other conferences
        CompSysTech '19: Proceedings of the 20th International Conference on Computer Systems and Technologies
        June 2019
        365 pages
        ISBN:9781450371490
        DOI:10.1145/3345252
        Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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        • UORB: University of Ruse, Bulgaria

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        New York, NY, United States

        Publication History

        Published: 21 June 2019

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        Author Tags

        1. DFA method
        2. MFDFA method
        3. RR-intervals
        4. fractal analysis
        5. multifractal analysis

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        • (2023)Gas Desorption Behaviors in the In Situ Gas Desorption Test of Organic-Rich Shales: Implication of Monofractality and MultifractalityEnergy & Fuels10.1021/acs.energyfuels.3c0263137:19(14867-14881)Online publication date: 26-Sep-2023
        • (2021)Fractal Analysis and Interpretation of Temporal Patterns of TSP and PM10 Mass Concentration over Tarkwa, GhanaEarth Systems and Environment10.1007/s41748-021-00237-25:3(635-654)Online publication date: 25-Jun-2021

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