Double stochastic opinion dynamics with fractional inflow of new opinions
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914876298887168 |
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| author | Gontis, Vygintas |
| author_facet | Gontis, Vygintas |
| contents | A recent analysis of empirical limit order flow data highlights the necessity for a more refined order flow model that integrates the power-law distribution of limit order cancellation times. These cancellation times follow a discrete probability mass function derived from the Tsallis $q$-exponential distribution, or equivalently, the second form of the Pareto distribution. By combining fractional L'{e}vy stable motion as the model for limit order inflow with the power-law distribution for cancellation times, we propose an innovative approach to modeling order imbalance in financial markets. We extend this model to a broader context, illustrating its applicability to opinion dynamics in social systems where opinions have a finite lifespan. This proposed model exemplifies a stochastic time series characterized by stationary increments and broken self-similarity. Consequently, it offers a novel framework for testing methods to evaluate long-range dependence in such time series. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_13206 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Double stochastic opinion dynamics with fractional inflow of new opinions Gontis, Vygintas Physics and Society A recent analysis of empirical limit order flow data highlights the necessity for a more refined order flow model that integrates the power-law distribution of limit order cancellation times. These cancellation times follow a discrete probability mass function derived from the Tsallis $q$-exponential distribution, or equivalently, the second form of the Pareto distribution. By combining fractional L'{e}vy stable motion as the model for limit order inflow with the power-law distribution for cancellation times, we propose an innovative approach to modeling order imbalance in financial markets. We extend this model to a broader context, illustrating its applicability to opinion dynamics in social systems where opinions have a finite lifespan. This proposed model exemplifies a stochastic time series characterized by stationary increments and broken self-similarity. Consequently, it offers a novel framework for testing methods to evaluate long-range dependence in such time series. |
| title | Double stochastic opinion dynamics with fractional inflow of new opinions |
| topic | Physics and Society |
| url | https://arxiv.org/abs/2407.13206 |