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.