Article
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Modeling Double Stochastic Opinion Dynamics with Fractional Inflow of New Opinions
Version 1
: Received: 29 July 2024 / Approved: 1 August 2024 / Online: 1 August 2024 (10:20:47 CEST)
How to cite: Gontis, V. Modeling Double Stochastic Opinion Dynamics with Fractional Inflow of New Opinions. Preprints 2024, 2024080032. https://doi.org/10.20944/preprints202408.0032.v1 Gontis, V. Modeling Double Stochastic Opinion Dynamics with Fractional Inflow of New Opinions. Preprints 2024, 2024080032. https://doi.org/10.20944/preprints202408.0032.v1
Abstract
Our recent analysis of empirical limit order flow data in financial markets reveals a power-law distribution in limit order cancellation times. These times are modeled using a discrete probability mass function derived from the Tsallis q-exponential distribution, closely aligned with the second form of the Pareto distribution. We elucidate this distinctive power-law statistical property through the lens of agent heterogeneity in trading activity and asset possession. Our study introduces a novel modeling approach that combines fractional Lévy stable motion for limit order inflow with this power-law distribution for cancellation times, significantly enhancing the prediction of order imbalances. This model not only addresses gaps in current financial market modeling but also extends to broader contexts such as opinion dynamics in social systems, capturing the finite lifespan of opinions. Characterized by stationary increments and a departure from self-similarity, our model provides a unique framework for exploring long-range dependencies in time series. This work paves the way for more precise financial market analyses and offers new insights into the dynamic nature of opinion formation in social systems.
Keywords
time series and signal analysis; discrete stochastic dynamics; scaling in socio-economic systems; fractional dynamics; quantitative finance
Subject
Physical Sciences, Mathematical Physics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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