dorsal/arxiv
View SchemaA nonextensive approach to the dynamics of financial observables
| Authors | Silvio M. Duarte Queiros, Luis G. Moyano, Jeferson de Souza, Constantino Tsallis |
|---|---|
| Categories | |
| ArXiv ID | physics/0601222 |
| URL | https://arxiv.org/abs/physics/0601222 |
| DOI | 10.1140/epjb/e2006-00205-y |
| Journal | Eur. Phys. J. B 55, 161 (2007) |
Abstract
We present results about financial market observables, specifically returns and traded volumes. They are obtained within the current nonextensive statistical mechanical framework based on the entropy $S_{q}=k\frac{1-\sum\limits_{i=1}^{W} p_{i} ^{q}}{1-q} (q\in \Re)$ ($S_{1} \equiv S_{BG}=-k\sum\limits_{i=1}^{W}p_{i} \ln p_{i}$). More precisely, we present stochastic dynamical mechanisms which mimic probability density functions empirically observed. These mechanisms provide possible interpretations for the emergence of the entropic indices $q$ in the time evolution of the corresponding observables. In addition to this, through multi-fractal analysis of return time series, we verify that the dual relation $q_{stat}+q_{sens}=2$ is numerically satisfied, $q_{stat}$ and $q_{sens}$ being associated to the probability density function and to the sensitivity to initial conditions respectively. This type of simple relation, whose understanding remains ellusive, has been empirically verified in various other systems.
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"abstract": "We present results about financial market observables, specifically returns\nand traded volumes. They are obtained within the current nonextensive\nstatistical mechanical framework based on the entropy\n$S_{q}=k\\frac{1-\\sum\\limits_{i=1}^{W} p_{i} ^{q}}{1-q} (q\\in \\Re)$ ($S_{1}\n\\equiv S_{BG}=-k\\sum\\limits_{i=1}^{W}p_{i} \\ln p_{i}$). More precisely, we\npresent stochastic dynamical mechanisms which mimic probability density\nfunctions empirically observed. These mechanisms provide possible\ninterpretations for the emergence of the entropic indices $q$ in the time\nevolution of the corresponding observables. In addition to this, through\nmulti-fractal analysis of return time series, we verify that the dual relation\n$q_{stat}+q_{sens}=2$ is numerically satisfied, $q_{stat}$ and $q_{sens}$ being\nassociated to the probability density function and to the sensitivity to\ninitial conditions respectively. This type of simple relation, whose\nunderstanding remains ellusive, has been empirically verified in various other\nsystems.",
"arxiv_id": "physics/0601222",
"authors": [
"Silvio M. Duarte Queiros",
"Luis G. Moyano",
"Jeferson de Souza",
"Constantino Tsallis"
],
"categories": [
"physics.data-an",
"cond-mat.stat-mech",
"q-fin.ST"
],
"doi": "10.1140/epjb/e2006-00205-y",
"journal_ref": "Eur. Phys. J. B 55, 161 (2007)",
"title": "A nonextensive approach to the dynamics of financial observables",
"url": "https://arxiv.org/abs/physics/0601222"
},
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