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 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.
Highlights
Many empirical data sets and theoretical models have been investigated using the tool of spectral analysis
We have considered trades occurring in the financial markets as point events driven by a point process proposed in [21,22,23]
We overview how the physically motivated point process proposed in [21,22,23] was applied to model trading activity and absolute returns in the financial markets
Summary
Many empirical data sets and theoretical models have been investigated using the tool of spectral analysis. 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. We present a novel result, which concerns understanding the nature of the self-similarity and long-range memory phenomenon from the perspective of fractional Lèvy stable motion We overview how the physically motivated point process proposed in [21,22,23] was applied to model trading activity and absolute returns in the financial markets. We discuss numerous extensions of the model into some related research topics, such as superstatistics and anomalous and non-homogeneous diffusion
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
