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Understanding the nature of the long--range memory phenomenon in socio-economic systems

Rytis Kazakevicius, Aleksejus Kononovicius, Bronislovas Kaulakys, Vygintas Gontis

posted on 06 August 2021

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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.


This manuscript analyzes our groups of Vilnius university's 20 years of contribution to the development of Econophysics. We provide an overview of our approach to understanding and modeling the long-range memory phenomenon in financial markets and other complex systems and share our most recent result.

Though the financial markets provide us with a vast amount of empirical data, the best model selection is still a big challenge for researchers. The widely used long-range memory and self-similarity estimators give varying values of the parameters as these estimators themselves are developed for the specific models of time series.

The proposed manuscript is based on Time-series and signals analysis; discrete, stochastic dynamics; Fractional dynamics. We seek to interpret the general properties of scaling in socio-economic systems that might value the broad interdisciplinary research community.