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Identifying stock market crashes by fuzzy measures of complexity
Bielinskyi, Andrii; Соловйов, Володимир Миколайович; Семеріков, Сергій Олексійович; Solovieva, Viktoria; Білінський, Андрій Іванович; Соловйова, Вікторія Володимирівна
Date:
2021-12-13
Abstract:
This study, for the first time, presents the possibility of using fuzzy set theory in combination with information theory and recurrent analysis to construct indicators (indicators-precursors) of crisis phenomena in complex nonlinear systems. In our study, we analyze the 4 most important crisis periods in the history of the stock market – 1929, 1987, 2008 and the COVID-19 pandemic in 2020. In particular, using the sliding window procedure, we analyze how the complexity of the studied crashes changes over time, and how it depends on events such as the global stock market crises. For comparative analysis, we take classical Shannon entropy, approximation and permutation entropy, recurrent diagrams, and their fuzzy alternatives. Each of the fuzzy modifications uses three membership functions: exponential, sigmoidal, and simple linear functions. Empirical results demonstrate the fact that the fuzzification of classical entropy and recurrence approaches opens up prospects for constructing effective and reliable indicators-precursors of critical events in the studied complex systems
Description:
1. Acharya, U.R., Sree, S.V., Chattopadhyay, S., Yu, W., & Ang, P.C.A.
(2011). Application of recurrence quantification analysis for the automated
identification of epileptic EEG signals. International journal of neural
systems, 21(03), 199-211. https://doi.org/10.1142/s0129065711002808
2. Aldalou, E., & Perçin, S. (2020). Application of integrated fuzzy
MCDM approach for financial performance evaluation of Turkish
technology sector. International Journal of Procurement Management,
13(1), 1-23. https://doi.org/10.1504/ijpm.2020.105198
3. Al-Sharhan, S., Karray, F., Gueaieb, W., & Basir, O. (2001). Fuzzy
entropy: a brief survey. In Proceedings of the 10th IEEE international
conference on fuzzy systems (Cat. No. 01CH37297): Vol. 3 (pp. 1135-1139).
IEEE. https://doi.org/10.1109/FUZZ.2001.1008855
4. Alves, P. (2019). Chaos in historical prices and volatilities with five-
dimensional Euclidean spaces. Chaos, Solitons & Fractals: X, 1, Article
100002. https://doi.org/10.1016/j.csfx.2019.100002
5. Argyroudis, G. S., & Siokis, F. M. (2019). Spillover effects of Great
Recession on Hong-Kong’s Real Estate Market: An analysis based on
Causality Plane and Tsallis Curves of Complexity–Entropy. Physica A:
Statistical
Mechanics
and
its
Applications,
524,
576–586.
https://doi.org/10.1016/j.physa.2019.04.052
6. Azami, H., Fernández, A., & Escudero, J. (2017). Refined multiscale
fuzzy entropy based on standard deviation for biomedical signal analysis.
Medical & Biological Engineering & Computing, 55(11), 2037–2052.
https://doi.org/10.1007/s11517-017-1647-5
7. Bandt, C., & Pompe, B. (2002). Permutation Entropy: A Natural
Complexity Measure for Time Series. Physical Review Letters, 88(17),
Article 174102. https://doi.org/10.1103/physrevlett.88.174102
8. Bastos, J. A., & Caiado, J. (2011). Recurrence quantification analysis
of global stock markets. Physica A: Statistical Mechanics and its Appli-
cations, 390(7), 1315–1325. https://doi.org/10.1016/j.physa.2010.12.008
9. Bielinskyi, A., Semerikov, S., Serdyuk, O., Solovieva, V.,
Soloviev, V., & Pichl, L. (2020). Econophysics of sustainability indices.
CEUR Workshop Proceedings, 2713, 372-392. http://ceur-ws.org/Vol-
2713/paper41.pdf
10. Bielinskyi, A., & Soloviev, V. (2018). Complex network precursors of
crashes and critical events in the cryptocurrency market. CEUR Workshop
Proceedings, 2292, 37-45. http://ceur-ws.org/Vol-2292/paper02.pdf
11. Bielinskyi, A., Soloviev, V., Semerikov, S., & Solovieva, V. (2019).
Detecting stock crashes using Levy distribution. CEUR Workshop
Proceedings, 2422, 420-433. http://ceur-ws.org/Vol-2422/paper34.pdf
12. Boccara, N. (2010). Modeling complex systems. Springer Science &
Business Media. https://doi.org/10.1007/978-1-4419-6562-2
13. Castiglioni, P., & Di Rienzo, M. (2008). How the threshold “r”
influences approximate entropy analysis of heart-rate variability. In
Proceedings of the 2008 Computers in Cardiology (pp. 561-564). IEEE.
https://doi.org/10.1109/CIC.2008.4749103
14. Chen, W., Wang, Z., Xie, H., & Yu, W. (2007). Characterization of
Surface EMG Signal Based on Fuzzy Entropy. IEEE Transactions on Neural
Systems
and
Rehabilitation
Engineering,
15(2),
266–272.
https://doi.org/10.1109/tnsre.2007.897025
15. Chen, W., Zhuang, J., Yu, W., & Wang, Z. (2009). Measuring
complexity using FuzzyEn, ApEn, and SampEn. Medical Engineering &
Physics, 31(1), 61–68. https://doi.org/10.1016/j.medengphy.2008.04.005
16. Collet, P., Eckmann, J. P., & Koch, H. (1981). Period doubling
bifurcations for families of maps on R n . Journal of Statistical Physics,
25(1), 1–14. https://doi.org/10.1007/bf01008475
17. De Luca, A., & Termini, S. (1972). A definition of a nonprobabilistic
entropy in the setting of fuzzy sets theory. Information and Control, 20(4),
301–312. https://doi.org/10.1016/s0019-9958(72)90199-4
18. Duran, N.D., Dale, R., Kello, C.T., Street, C.N.H., & Richardson, D.C.
(2013). Exploring the movement dynamics of deception. Frontiers in
Psychology, 4, Article 140. https://doi.org/10.3389/fpsyg.2013.00140
19. Eckmann, J. P., & Ruelle, D. (1985). Ergodic theory of chaos and
strange attractors. Reviews of Modern Physics, 57(3), 617–656.
https://doi.org/10.1103/revmodphys.57.617
20. Eckmann, J. P., Kamphorst, S. O., & Ruelle, D. (1987). Recurrence
Plots of Dynamical Systems. Europhysics Letters, 4(9), 973–977.
https://doi.org/10.1209/0295-5075/4/9/004
21. Elias, J., & Narayanan Namboothiri, V. N. (2013). Cross-recurrence
plot quantification analysis of input and output signals for the detection of
chatter
in
turning.
Nonlinear
Dynamics,
76(1),
255–261.
https://doi.org/10.1007/s11071-013-1124-0
22. Eroglu, D., McRobie, F. H., Ozken, I., Stemler, T., Wyrwoll, K. H.,
Breitenbach, S. F. M., Marwan, N., & Kurths, J. (2016). See–saw rela-
tionship of the Holocene East Asian–Australian summer monsoon. Nature
Communications, 7(1), Article 12929. https://doi.org/10.1038/ncomms12929
23. Farmer, J. D. (1982). Information Dimension and the Probabilistic
Structure of Chaos. Zeitschrift Für Naturforschung A, 37(11), 1304–1326.
https://doi.org/10.1515/zna-1982-1117
24. García-Ochoa, E., González-Sánchez, J., Acuña, N., & Euan, J. (2008).
Analysis of the dynamics of Intergranular corrosion process of sensitised 304
stainless steel using recurrence plots. Journal of Applied Electrochemistry,
39(5), 637–645. https://doi.org/10.1007/s10800-008-9702-4
25. Gardini, L., Lupini, R., & Messia, M. G. (1989). Hopf bifurcation
and transition to chaos in Lotka-Volterra equation. Journal of Mathematical
Biology, 27(3), 259–272. https://doi.org/10.1007/bf00275811
26. GitHub. (2021). Complex systems measures. https://github.com/
Butman2099/Complex-systems-measures
27. GitHub. (2021). EntropyHub: An open-source toolkit for entropic
time series analysis. https://github.com/MattWillFlood/EntropyHub
28. Graf, S. (1987). Statistically self-similar fractals. Probability Theory
and Related Fields, 74(3), 357–392. https://doi.org/10.1007/bf00699096
29. Grassberger, P., & Procaccia, I. (1983). Characterization of Strange
Attractors.
Physical
Review
Letters,
50(5),
346–349.
https://doi.org/10.1103/physrevlett.50.346
30. Grebogi, C., Ott, E., Pelikan, S., & Yorke, J. A. (1984). Strange
attractors that are not chaotic. Physica D: Nonlinear Phenomena, 13(1-2),
261-268. https://doi.org/10.1016/0167-2789(84)90282-3
31. Harris, P., Litak, G., Iwaniec, J., & Bowen, C. R. (2016). Recurrence
Plot and Recurrence Quantification of the Dynamic Properties of Cross-
Shaped Laminated Energy Harvester. Applied Mechanics and Materials,
849, 95–105. https://doi.org/10.4028/www.scientific.net/amm.849.95
32. He, S., Sun, K., & Wang, R. (2018). Fractional fuzzy entropy
algorithm and the complexity analysis for nonlinear time series. The
European Physical Journal Special Topics, 227(7), 943-957.
https://doi.org/10.1140/epjst/e2018-700098-x
33. Hou, Y., Aldrich, C., Lepkova, K., Machuca, L., & Kinsella, B.
(2016). Monitoring of carbon steel corrosion by use of electrochemical noise
and recurrence quantification analysis. Corrosion Science, 112, 63–72.
https://doi.org/10.1016/j.corsci.2016.07.009
34. Humeau-Heurtier, A. (2015). The Multiscale Entropy Algorithm and
Its
Variants:
A
Review.
Entropy,
17(5),
3110–3123.
https://doi.org/10.3390/e17053110
35. Hutchinson, J. E. (1981). Fractals and Self Similarity. Indiana
University
Mathematics
Journal,
30(5),
713-747.
https://www.jstor.org/stable/24893080
36. Ishizaki, R., & Inoue, M. (2020). Analysis of local and global
instability in foreign exchange rates using short-term information entropy.
Physica A: Statistical Mechanics and its Applications, 555, Article 124595.
https://doi.org/10.1016/j.physa.2020.124595
37. Iwaniec, J., Uhl, T., Staszewski, W. J., & Klepka, A. (2012).
Detection of changes in cracked aluminium plate determinism by recurrence
analysis. Nonlinear Dynamics, 70(1), 125–140. https://doi.org/10.1007/
s11071-012-0436-9
38. Jahanshahi, H., Yousefpour, A., Wei, Z., Alcaraz, R., & Bekiros, S.
(2019). A financial hyperchaotic system with coexisting attractors: Dynamic
investigation, entropy analysis, control and synchronization. Chaos, Solitons
& Fractals, 126, 66–77. https://doi.org/10.1016/j.chaos.2019.05.023
39. Kantz, H. (1994). A robust method to estimate the maximal
Lyapunov exponent of a time series. Physics Letters A, 185(1), 77–87.
https://doi.org/10.1016/0375-9601(94)90991-1
40. Konvalinka, I., Xygalatas, D., Bulbulia, J., Schjødt, U.,
Jegindø, E. M., Wallot, S., van Orden, G., & Roepstorff, A. (2011).
Synchronized arousal between performers and related spectators in a fire-
walking ritual. Proceedings of the National Academy of Sciences of the
United States of America, 108(20), 8514–8519. https://doi.org/10.1073/
pnas.1016955108
41. Lahmiri, S., & Bekiros, S. (2017). Disturbances and complexity in
volatility time series. Chaos, Solitons & Fractals, 105, 38–42.
https://doi.org/10.1016/j.chaos.2017.10.006
42. Lahmiri, S., & Bekiros, S. (2019). Nonlinear analysis of Casablanca
Stock Exchange, Dow Jones and S&P500 industrial sectors with a
comparison. Physica A: Statistical Mechanics and its Applications, 539,
Article 122923. https://doi.org/10.1016/j.physa.2019.122923
43. Lahmiri, S., & Bekiros, S. (2020). Randomness, Informational
Entropy, and Volatility Interdependencies among the Major World Markets:
The Role of the COVID-19 Pandemic. Entropy, 22(8), Article 833.
https://doi.org/10.3390/e22080833
44. Lahmiri, S., Bekiros, S., & Avdoulas, C. (2018). Time-dependent
complexity measurement of causality in international equity markets:
A spatial approach. Chaos, Solitons & Fractals, 116, 215–219.
https://doi.org/10.1016/j.chaos.2018.09.030
45. Lahmiri, S., Uddin, G. S., & Bekiros, S. (2017). Nonlinear dynamics
of equity, currency and commodity markets in the aftermath of the global
financial crisis. Chaos, Solitons & Fractals, 103, 342–346.
https://doi.org/10.1016/j.chaos.2017.06.019
46. Lam, W. S., Lam, W. H., Jaaman, S. H., & Liew, K. F. (2021).
Performance Evaluation of Construction Companies Using Integrated
Entropy–Fuzzy VIKOR Model. Entropy, 23(3), Article 320.
https://doi.org/10.3390/e23030320
47. Li, P., Liu, C., Li, K., Zheng, D., Liu, C., & Hou, Y. (2014).
Assessing the complexity of short-term heartbeat interval series by
distribution entropy. Medical & Biological Engineering & Computing,
53(1), 77–87. https://doi.org/10.1007/s11517-014-1216-0
48. Li, S., Zhao, Z., Wang, Y., & Wang, Y. (2011). Identifying spatial
patterns of synchronization between NDVI and climatic determinants using
joint recurrence plots. Environmental Earth Sciences, 64(3), 851–859.
https://doi.org/10.1007/s12665-011-0909-z
49. List of stock market crashes and bear markets. (2021, August 1).
In Wikipedia.
https://en.wikipedia.org/w/index.php?title=List_of_stock_
market_crashes_and_bear_markets
50. Longwic, R., Litak, G., & Sen, A. K. (2009). Recurrence Plots for
Diesel Engine Variability Tests. Zeitschrift Für Naturforschung A, 64(1–2),
96–102. https://doi.org/10.1515/zna-2009-1-214
51. Mandelbrot, B. B. (1985). Self-Affine Fractals and Fractal
Dimension. Physica Scripta, 32(4), 257–260. https://doi.org/10.1088/0031-
8949/32/4/001
52. Marwan, N., Trauth, M. H., Vuille, M., & Kurths, J. (2003).
Comparing modern and Pleistocene ENSO-like influences in NW Argentina
using nonlinear time series analysis methods. Climate Dynamics, 21(3–4),
317–326. https://doi.org/10.1007/s00382-003-0335-3
53. Marwan, N., Wessel, N., Meyerfeldt, U., Schirdewan, A., & Kurths, J.
(2002). Recurrence-plot-based measures of complexity and their application
to heart-rate-variability data. Physical Review E, 66(2), Article 026702.
https://doi.org/10.1103/physreve.66.026702
54. Moore, J. M., Corrêa, D. C., & Small, M. (2018). Is Bach’s brain a
Markov chain? Recurrence quantification to assess Markov order for short,
symbolic, musical compositions. Chaos: An Interdisciplinary Journal of
Nonlinear Science, 28(8), Article 085715. https://doi.org/10.1063/1.5024814
55. Nair, V., & Sujith, R. I. (2013). Identifying homoclinic orbits in the
dynamics of intermittent signals through recurrence quantification. Chaos:
An Interdisciplinary Journal of Nonlinear Science, 23(3), Article 033136.
https://doi.org/10.1063/1.4821475
56. Nichols, J., Trickey, S., & Seaver, M. (2006). Damage detection
using multivariate recurrence quantification analysis. Mechanical Systems
and Signal Processing, 20(2), 421–437. https://doi.org/10.1016/
j.ymssp.2004.08.007
57. Palmieri, F., & Fiore, U. (2009). A nonlinear, recurrence-based
approach to traffic classification. Computer Networks, 53(6), 761–773.
https://doi.org/10.1016/j.comnet.2008.12.015
58. Pham, T. D. (2016). Fuzzy recurrence plots. Europhysics Letters,
116(5), Article 50008. https://doi.org/10.1209/0295-5075/116/50008
59. Pham, T. D. (2019). Fuzzy weighted recurrence networks of time
series. Physica A: Statistical Mechanics and its Applications, 513, 409–417.
https://doi.org/10.1016/j.physa.2018.09.035
60. Pham, T. D. (2020). Fuzzy cross and fuzzy joint recurrence plots.
Physica A: Statistical Mechanics and its Applications, 540, Article 123026.
https://doi.org/10.1016/j.physa.2019.123026
61. Pham, T. D. (2020). Fuzzy recurrence entropy. Europhysics Letters,
130(4), Article 40004. https://doi.org/10.1209/0295-5075/130/40004
62. Pham, T. D. (2020). Fuzzy recurrence plots. In Fuzzy Recurrence
Plots and Networks with Applications in Biomedicine (pp. 29-55). Springer.
https://doi.org/10.1007/978-3-030-37530-0_4
63. Pham, T. D., Wardell, K., Eklund, A., & Salerud, G. (2019).
Classification of short time series in early Parkinsons disease with deep
learning of fuzzy recurrence plots. IEEE/CAA Journal of Automatica Sinica,
6(6), 1306–1317. https://doi.org/10.1109/jas.2019.1911774
64. Pincus, S. M. (1991). Approximate entropy as a measure of system
complexity. Proceedings of the National Academy of Sciences of the United
States of America, 88(6), 2297–2301. https://doi.org/10.1073/pnas.88.6.2297
65. Pincus, S. M., & Goldberger, A. L. (1994). Physiological time-series
analysis: what does regularity quantify? American Journal of Physiology-
Heart
and
Circulatory
Physiology,
266(4),
H1643–H1656.
https://doi.org/10.1152/ajpheart.1994.266.4.h1643
66. Pincus, S. M., & Huang, W. M. (1992). Approximate entropy:
Statistical properties and applications. Communications in Statistics –
Theory
and
Methods,
21(11),
3061–3077.
https://doi.org/10.1080/03610929208830963
67. Qian, Y., Yan, R., & Hu, S. (2014). Bearing Degradation Evaluation
Using Recurrence Quantification Analysis and Kalman Filter. IEEE
Transactions on Instrumentation and Measurement, 63(11), 2599–2610.
https://doi.org/10.1109/tim.2014.2313034
68. Rand, R., & Holmes, P. (1980). Bifurcation of periodic motions in
two weakly coupled van der Pol oscillators. International Journal of Non-
Linear Mechanics, 15(4–5), 387–399. https://doi.org/10.1016/0020-
7462(80)90024-4
69. Reinertsen, E., Osipov, M., Liu, C., Kane, J. M., Petrides, G., &
Clifford, G. D. (2017). Continuous assessment of schizophrenia using heart
rate and accelerometer data. Physiological Measurement, 38(7), 1456–1471.
https://doi.org/10.1088/1361-6579/aa724d
70. Richardson, D. C., & Dale, R. (2005). Looking to Understand: The
Coupling Between Speakers’ and Listeners’ Eye Movements and Its
Relationship to Discourse Comprehension. Cognitive Science, 29(6), 1045–
1060. https://doi.org/10.1207/s15516709cog0000_29
71. Richman, J. S., & Moorman, J. R. (2000). Physiological time-series
analysis using approximate entropy and sample entropy. American Journal
of Physiology-Heart and Circulatory Physiology, 278(6), H2039–H2049.
https://doi.org/10.1152/ajpheart.2000.278.6.h2039
72. Roncagliolo Barrera, P., Rodríguez Gómez, F., & García Ochoa, E.
(2019). Assessing of New Coatings for Iron Artifacts Conservation by
Recurrence
Plots
Analysis.
Coatings,
9(1),
Article
12.
https://doi.org/10.3390/coatings9010012
73. Rostaghi, M., & Azami, H. (2016). Dispersion Entropy: A Measure
for Time-Series Analysis. IEEE Signal Processing Letters, 23(5), 610–614.
https://doi.org/10.1109/lsp.2016.2542881
74. Ruelle, D. (1981). Small random perturbations of dynamical systems
and the definition of attractors. Communications in Mathematical Physics,
82(1), 137–151. https://doi.org/10.1007/bf01206949
75. Sanchez-Roger, M., Oliver-Alfonso, M. D., & Sanchís-Pedregosa, C.
(2019). Fuzzy Logic and Its Uses in Finance: A Systematic Review
Exploring Its Potential to Deal with Banking Crises. Mathematics, 7(11),
Article 1091. https://doi.org/10.3390/math7111091
76. Serrà, J., Serra, X., & Andrzejak, R. G. (2009). Cross recurrence
quantification for cover song identification. New Journal of Physics, 11,
Article 093017. https://doi.org/10.1088/1367-2630/11/9/093017
77. Shannon, C. E. (1948). A Mathematical Theory of Communication.
Bell System Technical Journal, 27(3), 379–423. https://doi.org/10.1002/
j.1538-7305.1948.tb01338.x
78. Shao, W., & Wang, J. (2020). Does the “ice-breaking” of South
and North Korea affect the South Korean financial market? Chaos,
Solitons & Fractals, 132, Article 109564. https://doi.org/10.1016/
j.chaos.2019.109564
79. Shaw, R. (1981). Strange Attractors, Chaotic Behavior, and
Information Flow. Zeitschrift Für Naturforschung A, 36(1), 80–112.
https://doi.org/10.1515/zna-1981-0115
80. Shi, B., Wang, L., Yan, C., Chen, D., Liu, M., & Li, P. (2019).
Nonlinear heart rate variability biomarkers for gastric cancer severity:
A pilot
study.
Scientific
Reports,
9(1),
Article
13833.
https://doi.org/10.1038/s41598-019-50358-y
81. Silva, D. F., De Souza, V. M., & Batista, G. E. (2013). Time series
classification using compression distance of recurrence plots. In Proceedings
of 2013 IEEE 13th International Conference on Data Mining (pp. 687-696).
IEEE. https://doi.org/10.1109/ICDM.2013.128
82. Soloviev, V., & Belinskiy, A. (2018). Complex systems theory and
crashes of cryptocurrency market. In V. Ermolayev, M. Suárez-Figueroa,
V. Yakovyna, H. Mayr, M. Nikitchenko, & A. Spivakovsky (Eds.),
Communications in Computer and Information Science: Vol. 1007.
Information and Communication Technologies in Education, Research, and
Industrial Applications (pp. 276-297). Springer. https://doi.org/10.1007/978-
3-030-13929-2_14
83. Soloviev, V., & Belinskij, A. (2018). Methods of nonlinear
dynamics and the construction of cryptocurrency crisis phenomena
precursors. CEUR Workshop Proceedings, 2104, 116-127. http://ceur-
ws.org/Vol-2104/paper_175.pdf
84. Soloviev, V., Bielinskyi, A., & Kharadzjan, N. (2020). Coverage of
the coronavirus pandemic through entropy measures. CEUR Workshop
Proceedings, 2832, 24-42. http://ceur-ws.org/Vol-2832/paper02.pdf
85. Soloviev, V., Bielinskyi, A., Serdyuk, O., Solovieva, V., &
Semerikov, S. (2020). Lyapunov exponents as indicators of the stock market
crashes. CEUR Workshop Proceedings, 2732, 455-470. http://ceur-
ws.org/Vol-2732/20200455.pdf
86. Soloviev, V., Bielinskyi, A., & Solovieva, V. (2019). Entropy
analysis of crisis phenomena for DJIA index. CEUR Workshop Proceedings,
2393, 434-449. http://ceur-ws.org/Vol-2393/paper_375.pdf
87. Soloviev, V., Serdiuk, O., Semerikov, S., & Kohut-Ferens, O.
(2019). Recurrence entropy and financial crashes. Advances in Economics,
Business
and
Management
Research,
99,
385-388.
https://dx.doi.org/10.2991/mdsmes-19.2019.73
88. Stangalini, M., Ermolli, I., Consolini, G., & Giorgi, F. (2017).
Recurrence quantification analysis of two solar cycle indices. Journal of
Space
Weather
and
Space
Climate,
7,
Article
A5.
https://doi.org/10.1051/swsc/2017004
89. Stender, M., Oberst, S., Tiedemann, M., & Hoffmann, N. (2019).
Complex machine dynamics: systematic recurrence quantification analysis of
disk brake vibration data. Nonlinear Dynamics, 97(4), 2483–2497.
https://doi.org/10.1007/s11071-019-05143-x
90. Strozzi, F., Zaldı́ Var, J. M., & Zbilut, J. P. (2002). Application of
nonlinear time series analysis techniques to high-frequency currency
exchange data. Physica A: Statistical Mechanics and its Applications, 312(3–
4), 520–538. https://doi.org/10.1016/s0378-4371(02)00846-4
91. Takens, F. (1981). Detecting strange attractors in turbulence. In
D. Rand, & L. Young (Eds.), Lecture Notes in Mathematics: Vol. 898.
Dynamical systems and turbulence, Warwick 1980 (pp. 366-381). Springer-
Verlag. https://doi.org/10.1007/BFb0091924
92. Voss, A., Schroeder, R., Vallverdu, M., Cygankiewicz, I., Vazquez, R.,
de Luna, A. B., & Caminal, P. (2008). Linear and nonlinear heart rate
variability risk stratification in heart failure patients. In Proceedings of the
2008 Computers in Cardiology (pp. 557-560). IEEE. https://doi.org/10.1109/
CIC.2008.4749102
93. Wang, G., & Wang, J. (2017). New approach of financial volatility
duration dynamics by stochastic finite-range interacting voter system.
Chaos: An Interdisciplinary Journal of Nonlinear Science, 27(1), Article
013117. https://doi.org/10.1063/1.4974216
94. Wang, Y., Zheng, S., Zhang, W., Wang, G., & Wang, J. (2018).
Fuzzy entropy complexity and multifractal behavior of statistical physics
financial dynamics. Physica A: Statistical Mechanics and its Applications,
506, 486–498. https://doi.org/10.1016/j.physa.2018.04.086
95. Webber, C. L., & Zbilut, J. P. (1994). Dynamical assessment of
physiological systems and states using recurrence plot strategies. Journal of
Applied Physiology, 76(2), 965–973. https://doi.org/10.1152/jappl.1994.76.2.965
96. Xie, H. B., He, W. X., & Liu, H. (2008). Measuring time series
regularity using nonlinear similarity-based sample entropy. Physics Letters
A, 372(48), 7140–7146. https://doi.org/10.1016/j.physleta.2008.10.049
97. Xie, H. B., Sivakumar, B., Boonstra, T. W., & Mengersen, K.
(2018). Fuzzy Entropy and Its Application for Enhanced Subspace Filtering.
IEEE
Transactions
on
Fuzzy
Systems,
26(4),
1970–1982.
https://doi.org/10.1109/tfuzz.2017.2756829
98. Yang, Y. G., Pan, Q. X., Sun, S. J., & Xu, P. (2015). Novel Image
Encryption based on Quantum Walks. Scientific Reports, 5(1), Article 7784.
https://doi.org/10.1038/srep07784
99. Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338–
353. https://doi.org/10.1016/S0019-9958(65)90241-X
100. Zaitouny, A., Walker, D. M., & Small, M. (2019). Quadrant scan for
multi-scale transition detection. Chaos: An Interdisciplinary Journal of
Nonlinear
Science,
29(10),
Article
103117.
https://doi.org/10.1063/1.5109925
101. Zbilut, J. P., & Marwan, N. (2008). The Wiener–Khinchin theorem
and recurrence quantification. Physics Letters A, 372(44), 6622–6626.
https://doi.org/10.1016/j.physleta.2008.09.027
102. Zhang, Z., Xiang, Z., Chen, Y., & Xu, J. (2020). Fuzzy permutation
entropy derived from a novel distance between segments of time series.
AIMS Mathematics, 5(6), 6244–6260. https://doi.org/10.3934/math.2020402
103. Zhao, H., Deng, W., Yao, R., Sun, M., Luo, Y., & Dong, C. (2017).
Study on a novel fault diagnosis method based on integrating EMD, fuzzy
entropy, improved PSO and SVM. Journal of Vibroengineering, 19(4),
2562–2577. https://doi.org/10.21595/jve.2017.18052
104. Zhao, X., & Zhang, P. (2020). Multiscale horizontal visibility
entropy: Measuring the temporal complexity of financial time series. Physica
A: Statistical Mechanics and its Applications, 537, Article 122674.
https://doi.org/10.1016/j.physa.2019.122674
105. Zhao, Z. Q., Li, S. C., Gao, J. B., & Wang, Y. L. (2011). Identifying
Spatial Patterns and Dynamics of Climate Change Using Recurrence
Quantification Analysis: A Case Study of Qinghai–Tibet Plateau.
International Journal of Bifurcation and Chaos, 21(04), 1127-1139.
https://doi.org/10.1142/s0218127411028933
106. Zhou, C., & Zhang, W. (2015). Recurrence Plot Based Damage
Detection Method by Integrating T 2 Control Chart. Entropy, 17(5), 2624-
2641. https://doi.org/10.3390/e17052624
107. Zhou, Q., & Shang, P. (2020). Weighted multiscale cumulative
residual Rényi permutation entropy of financial time series. Physica A:
Statistical Mechanics and its Applications, 540, Article 123089.
https://doi.org/10.1016/j.physa.2019.123089
108. Zhou, R., Wang, X., Wan, J., & Xiong, N. (2021). EDM-Fuzzy: An
Euclidean Distance Based Multiscale Fuzzy Entropy Technology for Diagnosing Faults of Industrial Systems. IEEE Transactions on Industrial Informatics, 17(6), 4046–4054. https://doi.org/10.1109/tii.2020.3009139
109. Zolotova, N. V., & Ponyavin, D. I. (2006). Phase asynchrony of the north-south sunspot activity. Astronomy & Astrophysics, 449(1), L1–L4. https://doi.org/10.1051/0004-6361:200600013
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