A new tool to detect financial data scaling - Bianchi, Sergio; Pianese, Augusto; Frezza, Massimiliano; Angelini, Daniele (Frontiers in Applied Mathematics and Statistics, 2025)
The assumption of frictionless markets has long been debated, drawing interest from scholars and practitioners alike. Market liquidity is a central theme in this regard; it is traditionally assessed through transaction costs, volume, price-based, and market-impact measures. In contrast, the Fractal Market Hypothesis (FMH) suggests that liquidity emerges from the heterogeneity of investment time scales among participants, with liquidity shortages arise when traders converge on the same time horizons, particularly the short-term one which typically occurs during volatile periods. While current methods to asses liquidity often rely on single moments, which may provide limited insights, a novel methodology that considers the whole distributions and compares log-returns across pairs of time scales is discussed and implemented in this work. A Matlab-based algorithm is built that provides as output a dynamical estimation of the pairwise self-similarity of the scaled distributions. The lower the self-similarity parameter the higher the potential liquidity shortage.