Spurious Memory in Non-Equilibrium Stochastic Models of Imitative Behavior

Authored by Aleksejus Kononovicius

Date Published: 2017

DOI: 10.3390/e19080387

Sponsors: No sponsors listed

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Model Documentation: Other Narrative Mathematical description

Model Code URLs: Model code not found

Abstract

The origin of the long-range memory in non-equilibrium systems is still an open problem as the phenomenon can be reproduced using models based on Markov processes. In these cases, the notion of spurious memory is introduced. A good example of Markov processes with spurious memory is a stochastic process driven by a non-linear stochastic differential equation (SDE). This example is at odds with models built using fractional Brownian motion (fBm). We analyze the differences between these two cases seeking to establish possible empirical tests of the origin of the observed long-range memory. We investigate probability density functions (PDFs) of burst and inter-burst duration in numerically-obtained time series and compare with the results of fBm. Our analysis confirms that the characteristic feature of the processes described by a one-dimensional SDE is the power-law exponent 3/2 of the burst or inter-burst duration PDF. This property of stochastic processes might be used to detect spurious memory in various non-equilibrium systems, where observed macroscopic behavior can be derived from the imitative interactions of agents.

Tags

Agent-based modeling statistical physics time stochastic modeling Long-range memory Fluctuations Financial-markets Equations Spurious memory Non-equilibrium systems Markov processes First passage times Fractional brownian-motion Markov-processes Hurst exponents