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

A new nonparametric and distribution-based 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 us to test the statistical significance of the scaling exponent that possibly characterizes each pair of time scales, and to study the link between self-similarity and liquidity, the core assumption of the Fractal Market Hypothesis (FMH). The method can support financial operators in the selection of the investment horizons to be preferred as well as regulators in the adoption of guidelines to ensure 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