发表机构
Institute of Physics, Federal University of Rio Grande do Sul（南里奥格兰德联邦大学物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究对比幂律与q-高斯对金融收益分布的描述效果，发现幂律在极端尾部拟合更优，但q-高斯可全局描述分布，还能表征统计 regime 转变，是更实用的金融收益统计演化框架。
AI 中文摘要
金融市场是复杂系统，其收益分布呈现重尾特征，传统上用幂律描述。基于Tsallis非广延统计力学的替代框架允许用单一q-高斯函数形式表示分布的中心区域和尾部。本研究针对巴西、美国的股票市场，以及传统资产和加密货币，在不同时间尺度上系统比较这两种描述。q-高斯参数采用矩比法估计，幂律参数通过渐近区域的最大似然估计得到。拟合质量通过拟合优度度量、自举重采样和Vuong检验评估。当分析仅局限于极端尾部时，幂律通常提供更好的描述，这与q-高斯自身的渐近幂律行为预期一致。然而，这种优势不足以抵消q-高斯的主要优势：它能在所有研究的时间尺度上对整个分布（包括中心峰、主体和尾部）提供一致的描述。此外，参数q的演化能简单直接地表征聚合高斯性以及重尾与短尾统计 regime 之间的转变，无需对分布的不同区域分别拟合。这些结果表明，尽管幂律仍特别适用于描述极端事件，但q-高斯为表征金融收益的统计演化提供了更广泛、更实用的框架。
英文摘要
Financial markets are complex systems whose return distributions exhibit heavy tails, traditionally described by power laws. An alternative framework based on Tsallis nonextensive statistical mechanics allows both the central region and the tails of the distribution to be represented by a single q-Gaussian functional form. In this work, we systematically compare these two descriptions across different time scales, considering stock markets from Brazil and the United States, as well as traditional assets and cryptocurrencies. The q-Gaussian parameters are estimated using the method of moments ratio, whereas the power-law parameters are obtained by maximum likelihood estimation in the asymptotic region. The quality of the fits is assessed using goodness-of-fit measures, bootstrap resampling, and the Vuong test. When the analysis is restricted exclusively to the extreme tails, the power law generally provides a better description, as expected from the asymptotic power-law behavior of the q-Gaussian itself. However, this superiority is not sufficiently pronounced to outweigh the main advantage of the q-Gaussian: its ability to provide a consistent description of the entire distribution, including the central peak, bulk, and tails, over all investigated time scales. Moreover, the evolution of the parameter $q$ offers a simple and direct characterization of aggregational Gaussianity and of the transition between heavy- and short-tailed statistical regimes, without requiring separate fits for different regions of the distribution. These results indicate that, although the power law remains particularly suitable for describing extreme events, the q-Gaussian provides a broader and more practical framework for characterizing the statistical evolution of financial returns.
Comments22 pages, 11 figures
