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The modeling of power-law statistical properties, including long-range memory observed in
vastly different systems, remains an open problem in mathematics, physics, biology, and other
sciences. Any successful theoretical model of a real system should reproduce observed
statistical features. In socio-economic systems, the only source of information about the system
dynamics is those statistical properties, as the interactions on the agent-level are generally
unknown. Thus instead, one should make assumptions and check the resulting theoretical
models against the empirically known statistical properties. It is the hardest to satisfy the long-
range memory property requirement.
In our work, we have relied on multi-fractal Markov processes, in which the increments are
uncorrelated, unlike in fractional Brownian motion. Starting from the 1/f noise in physical
systems and properties of non-linear stochastic differential equations, we proposed the
explanation of long-range memory of volatility in the financial markets. Using this new
interpretation of the observed spurious long-range memory, we have proposed a
consentaneous agent-based financial market model, which was able to reproduce the power-
law statistical properties of absolute return precisely.
Though the spurious long-range memory property of volatility spans for the very long time
scales, in the high-frequency order flow data, one observes statistical properties, which can
probably be explained only by correlated stochastic increments. We seek to define novel
empirical methods, which would allow us to discern whether the observed long-range memory in
physical and social systems results from a Markov process or a stochastic process with
correlated increments. The first passage time or burst and inter-burst duration statistical
analysis is the main idea we want to explore seeking to extend widely used long-range memory estimators.
Vygintas Gontis studied theoretical physics at Vilnius University. Then he started his research career at the Institute of Physics of the Lithuanian Academy of Science, later at the Institute of Theoretical Physics and Astronomy. He wrote his Ph.D. thesis „Radiation Properties of Impurities in the Thermonuclear Plasma” at Vilnius University under the supervision of Prof. Zenonas Rudzikas and Prof. V.S. Lisitca from I.V. Kurchatov Institute of Atomic Energy. Later Vygintas Gontis was involved in the research of dynamically chaotic classical and quantum systems. At the beginning of the regained independence of Lithuania, Vygintas Gontis was working at the Government of Lithuania as Director-General of the Agency for Science, Higher Education, and Technologies, later at the Institute of Economics and Privatization. With the support of Lithuanian Scientific Society, Vygintas Gontis was directly involved in the development of Nacional science and higher education legislation. During this period, he spent for moths as an intern in the Nacional Science Foundation of the US. In the last 20 years, Vygintas Gontis has been working in the interdisciplinary field of Econophysics at the Institute of Theoretical Physics and Astronomy of Vilnius University. In 2015, he got the opportunity to spend a year at the Center or Polymer Studies of the Boston University led by Prof. H.E Stanley. He is the head of the Group of Complex Physical and Social Systems. The main research interests of Vygintas Gontis and his group are devoted to the agent-based and stochastic modeling and the application of statistical physics for the empirical analysis and
modeling of social systems in general.