Spurious versus real long-range memory in social systems
With Vygintas Gontis, Research Professor at Vilnius University, Institute of Theoretical Physics and Astronomy
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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.
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