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On anomalous distributions in intra-day financial time series and Non-extensive Statistical Mechanics

Silvio M. Duarte Queiros
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Abstract

In this paper one studies the distribution of log-returns (tick-by-tick) in the Lisbon stock market and shows that it is well adjusted by the solution of the equation, {$\frac{dp_{x}}{d| x|}=-β_{q^{\prime }}p_{x}^{q^{\prime}}-(β_{q}-β_{q^{\prime}}) p_{x}^{q}$}, which corresponds to a generalization of the differential equation which has as solution the power-laws that optimise the entropic form $S_{q}=-k \frac{1-\int p_{x}^{q} dx}{1-q}$, base of present non-extensive statistical mechanics.

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Silvio M. Duarte Queiros. 2004-03-24. On anomalous distributions in intra-day financial time series and Non-extensive Statistical Mechanics. https://arxiv.org/abs/cond-mat/0403624

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