A distribution-based method to gauge market liquidity through scale invariance between investment horizons

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 expo- nent that possibly characterizes each pair of time scales and to analyze the link between self-similarity and liquidity, the core assumption of the fractal mar- ket 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.