A nonparametric method is developed to detect self‐similarity among the rescaled distributions of the log‐price variations over a number of time scales. The procedure allows to test the statistical significance of the scaling exponent that possibly characterizes each pair of time scales and to analyze the link between self‐similarity and liquidity, the core assumption of the fractal market hypothesis. The method can support financial operators in the selection of the investment horizons as well as regulators in the adoption of guidelines to improve the stability of markets. The analysis performed on the S&P500 reveals a very complex, time‐changing scaling structure, which confirms the link between market liquidity and self‐similarity.

中文翻译：

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基于分布的方法，通过投资范围之间的规模不变性来衡量市场流动性

开发了一种非参数方法来检测多个时间范围内对数价格变化的重新定标分布之间的自相似性。该程序可以测试可能表征每对时间尺度的定标指数的统计显着性，并分析自相似性和流动性之间的联系，这是分形市场假设的核心假设。该方法可以为金融运营商选择投资范围提供支持，也可以为监管机构提供采用准则以提高市场稳定性的支持。在S＆P500上进行的分析揭示了一个非常复杂的，时变的缩放结构，这确认了市场流动性和自相似性之间的联系。