Understanding the nature of the long-range memory phenomenon in socioeconomic systems
arXiv:2108.02506 · doi:10.3390/e23091125
Abstract
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 actual long-range memory process or just a consequence of 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 ARFIMA sample series. Our newly obtained results seem indicate that new estimators of self-similarity and long-range memory for analyzing systems with non-Gaussian distributions have to be developed.
29 pages, 9 figures, 190 references
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Cited by in corpus (5)
- Anomalous diffusion and long-range memory in the scaled voter model
- Order flow in the financial markets from the perspective of the Fractional Lévy stable motion
- noise from the sequence of nonoverlapping rectangular pulses
- noise in semiconductors arising from the heterogeneous detrapping process of individual charge carriers
- Resemblance of the power-law scaling behavior of a non-Markovian and nonlinear point processes