A. Delgado-Bonal and Á.G. López Physica A 569 (2021) 125770
Funding
This research received no external funding. As a matter of fact, this research did not receive any funding whatsoever.
References
[1] M. Mitchell, Complexity: A Guided Tour, first ed., Oxford University Press, 2011.
[2] J. Kwapień, S. Drożdż, Physical approach to complex systems, Phys. Rep. 515 (3) (2012) 115–226, http://dx.doi.org/10.1016/j.physrep.2012.01.007.
[3] R. Gębarowski, P. Oświęcimka, M. Wątorek, S. Drożdż, Detecting correlations and triangular arbitrage opportunities in the forex by means of
multifractal detrended cross-correlations analysis, Nonlinear Dynam. 98 (3) (2019) 2349–2364, http://dx.doi.org/10.1007/s11071-019-05335-5.
[4] G.J. Chaitin, Randomness and mathematical proof, Sci. Am. 232 (1975) 47–52, http://dx.doi.org/10.1038/scientificamerican0575-47.
[5] A. Kolmogorov, A new metric invariant of transient dynamical systems and automorphisms in Lebesgue spaces, Dokl. Akad. Nauk SSSR 119.61
(1958) 864.
[6] Y. Sinai, On the notion of entropy of a dynamical system, Dokl. Russ. Acad. Sci. 124 (1959) 768–771.
[7] P. Grassberger, I. Procaccia, Estimation of the Kolmogorov entropy from a chaotic signal, Phys. Rev. A 28 (1983) 2591–2593, http://dx.doi.org/
10.1103/PhysRevA.28.2591.
[8] J.-P. Eckmann, D. Ruelle, Ergodic theory of chaos and strange attractors, Rev. Modern Phys. 57 (1985) 617–656.
[9] S.M. Pincus, Approximate entropy as a measure of system complexity., Proc. Natl. Acad. Sci. 88 (6) (1991) 2297–2301, http://dx.doi.org/10.
1073/pnas.88.6.2297.
[10] A. Delgado-Bonal, A. Marshak, Approximate entropy and sample entropy: A comprehensive tutorial, Entropy 21 (6) (2019) 541, http:
//dx.doi.org/10.3390/e21060541.
[11] A. Delgado-Bonal, Quantifying the randomness of the stock markets, Sci. Rep. 9 (1) (2019) 12761, http://dx.doi.org/10.1038/s41598-019-49320-9.
[12] A.M. Fraser, H.L. Swinney, Independent coordinates for strange attractors from mutual information, Phys. Rev. A 33 (1986) 1134–1140,
http://dx.doi.org/10.1103/PhysRevA.33.1134.
[13] M.B. Kennel, R. Brown, H.D.I. Abarbanel, Determining embedding dimension for phase-space reconstruction using a geometrical construction,
Phys. Rev. A 45 (1992) 3403–3411, http://dx.doi.org/10.1103/PhysRevA.45.3403.
[14] M. Perc, The dynamics of human gait, Eur. J. Phys. 26 (3) (2005) 525–534, http://dx.doi.org/10.1088/0143-0807/26/3/017.
[15] J. Bolea, R. Bailón, E. Pueyo, On the standardization of approximate entropy: Multidimensional approximate entropy index evaluated on
short-term HRV time series, Complexity 2018 (2018) 4953273, http://dx.doi.org/10.1155/2018/4953273.
[16] M. Costa, A.L. Goldberger, C.-K. Peng, Multiscale entropy analysis of complex physiologic time series, Phys. Rev. Lett. 89 (2002) 068102,
http://dx.doi.org/10.1103/PhysRevLett.89.068102.
[17] M.D. Costa, A.L. Goldberger, Generalized multiscale entropy analysis: Application to quantifying the complex volatility of human heartbeat time
series, Entropy 17 (3) (2015) 1197–1203, http://dx.doi.org/10.3390/e17031197.
[18] J.S. Richman, J.R. Moorman, Physiological time-series analysis using approximate entropy and sample entropy, Am. J. Physiol.-Heart Circ. Physiol.
278 (6) (2000) H2039–H2049, http://dx.doi.org/10.1152/ajpheart.2000.278.6.H2039.
[19] A. Delgado-Bonal, On the use of complexity algorithms: A cautionary lesson from climate research, Sci. Rep. 10 (1) (2020) 5092, http:
//dx.doi.org/10.1038/s41598-020-61731-7.
[20] S. Pincus, B.H. Singer, Randomness and degrees of irregularity, Proc. Natl. Acad. Sci. 93 (5) (1996) 2083–2088, http://dx.doi.org/10.1073/pnas.
93.5.2083.
[21] J.F. Restrepo, G. Schlotthauer, M.E. Torres, Maximum approximate entropy and r threshold: A new approach for regularity changes detection,
Physica A 409 (2014) 97–109, http://dx.doi.org/10.1016/j.physa.2014.04.041.
[22] S. Pincus, R.E. Kalman, Not all (possibly) “random” sequences are created equal, Proc. Natl. Acad. Sci. 94 (8) (1997) 3513–3518, http:
//dx.doi.org/10.1073/pnas.94.8.3513.
[23] Y.-C. Zhang, Complexity and 1/f noise. A phase space approach, J. Physique I 1 (1991) 971–977, http://dx.doi.org/10.1051/jp1:1991180.
[24] H.C. Fogedby, On the phase space approach to complexity, J. Stat. Phys. 69 (1) (1992) 411–425, http://dx.doi.org/10.1007/BF01053799.
[25] A. Humeau-Heurtier, The multiscale entropy algorithm and its variants: A review, Entropy 17 (5) (2015) 3110–3123, http://dx.doi.org/10.3390/
e17053110.
[26] J. Xia, P. Shang, Multiscale entropy analysis of financial time series, Fluct. Noise Lett. 11 (04) (2012) 1250033, http://dx.doi.org/10.1142/
S0219477512500332.
[27] M. Costa, A. Goldberger, C.-K. Peng, Multiscale entropy of biological signals, Phys. Rev. E (3) 71 (2005) 021906, http://dx.doi.org/10.1103/
PhysRevE.71.021906.
[28] M. Xu, P. Shang, Analysis of financial time series using multiscale entropy based on skewness and kurtosis, Physica A 490 (2018) 1543–1550,
http://dx.doi.org/10.1016/j.physa.2017.08.136.
[29] Y. Liu, Y. Lin, J. Wang, P. Shang, Refined generalized multiscale entropy analysis for physiological signals, Physica A 490 (2018) 975–985,
http://dx.doi.org/10.1016/j.physa.2017.08.047.
[30] P. Jorion, Predicting volatility in the foreign exchange market, J. Finance 50 (2) (1995) 507–528.
[31] S.R. Bentes, R. Menezes, D.A. Mendes, Long memory and volatility clustering: Is the empirical evidence consistent across stock markets? Physica
A 387 (2008) 3826–3830, http://dx.doi.org/10.1016/j.physa.2008.01.046.
[32] X. Zhao, C. Liang, N. Zhang, P. Shang, Quantifying the multiscale predictability of financial time series by an information-theoretic approach,
Entropy 21 (7) (2019) http://dx.doi.org/10.3390/e21070684.
[33] S.-D. Wu, C.-W. Wu, S.-G. Lin, C.-C. Wang, K.-Y. Lee, Time series analysis using composite multiscale entropy, Entropy 15 (3) (2013) 1069–1084,
http://dx.doi.org/10.3390/e15031069.
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