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Understanding the Nature of the Long-Range Memory Phenomenon in Socioeconomic Systems

Institute of Theoretical Physics and Astronomy, Vilnius University, Sauletekio al. 3, 10257 Vilnius, Lithuania
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Authors to whom correspondence should be addressed.
These authors contributed equally to this work.
Academic Editor: Ryszard Kutner
Entropy 2021, 23(9), 1125; https://doi.org/10.3390/e23091125
Received: 4 August 2021 / Revised: 25 August 2021 / Accepted: 25 August 2021 / Published: 29 August 2021
(This article belongs to the Special Issue Three Risky Decades: A Time for Econophysics?)
In the face of the upcoming 30th anniversary of econophysics, we review our contributions and other related works on the modeling of the long-range memory phenomenon in physical, economic, and other social complex systems. Our group has shown that the long-range memory phenomenon can be reproduced using various Markov processes, such as point processes, stochastic differential equations, and agent-based models—reproduced well enough to match other statistical properties of the financial markets, such as return and trading activity distributions and first-passage time distributions. Research has lead us to question whether the observed long-range memory is a result of the actual long-range memory process or just a consequence of the non-linearity of Markov processes. As our most recent result, we discuss the long-range memory of the order flow data in the financial markets and other social systems from the perspective of the fractional Lèvy stable motion. We test widely used long-range memory estimators on discrete fractional Lèvy stable motion represented by the auto-regressive fractionally integrated moving average (ARFIMA) sample series. Our newly obtained results seem to indicate that new estimators of self-similarity and long-range memory for analyzing systems with non-Gaussian distributions have to be developed. View Full-Text
Keywords: long-range memory; 1/f noise; absolute value estimator; anomalous diffusion; ARFIMA; first-passage times; fractional Lèvy stable motion; Higuchi’s method; mean squared displacement; multiplicative point process long-range memory; 1/f noise; absolute value estimator; anomalous diffusion; ARFIMA; first-passage times; fractional Lèvy stable motion; Higuchi’s method; mean squared displacement; multiplicative point process
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MDPI and ACS Style

Kazakevičius, R.; Kononovicius, A.; Kaulakys, B.; Gontis, V. Understanding the Nature of the Long-Range Memory Phenomenon in Socioeconomic Systems. Entropy 2021, 23, 1125. https://doi.org/10.3390/e23091125

AMA Style

Kazakevičius R, Kononovicius A, Kaulakys B, Gontis V. Understanding the Nature of the Long-Range Memory Phenomenon in Socioeconomic Systems. Entropy. 2021; 23(9):1125. https://doi.org/10.3390/e23091125

Chicago/Turabian Style

Kazakevičius, Rytis, Aleksejus Kononovicius, Bronislovas Kaulakys, and Vygintas Gontis. 2021. "Understanding the Nature of the Long-Range Memory Phenomenon in Socioeconomic Systems" Entropy 23, no. 9: 1125. https://doi.org/10.3390/e23091125

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