{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:46:02Z","timestamp":1753890362285,"version":"3.41.2"},"reference-count":24,"publisher":"Frontiers Media SA","license":[{"start":{"date-parts":[[2025,2,17]],"date-time":"2025-02-17T00:00:00Z","timestamp":1739750400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["frontiersin.org"],"crossmark-restriction":true},"short-container-title":["Front. Appl. Math. Stat."],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3389\/fams.2025.1527750","type":"journal-article","created":{"date-parts":[[2025,2,17]],"date-time":"2025-02-17T06:48:54Z","timestamp":1739774934000},"update-policy":"https:\/\/doi.org\/10.3389\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["A new tool to detect financial data scaling"],"prefix":"10.3389","volume":"11","author":[{"given":"Sergio","family":"Bianchi","sequence":"first","affiliation":[]},{"given":"Augusto","family":"Pianese","sequence":"additional","affiliation":[]},{"given":"Massimiliano","family":"Frezza","sequence":"additional","affiliation":[]},{"given":"Daniele","family":"Angelini","sequence":"additional","affiliation":[]}],"member":"1965","published-online":{"date-parts":[[2025,2,17]]},"reference":[{"key":"B1","first-page":"375","article-title":"Liquidity, Efficiency and the 2007 \u2212 2008 global financial crisis","volume":"19","author":"Bianchi","year":"2018","journal-title":"Ann Econ Finance"},{"key":"B2","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1016\/0304-405X(86)90065-6","article-title":"Asset pricing and the bid-ask spread","volume":"17","author":"Amihud","year":"1986","journal-title":"J Financ Econ"},{"key":"B3","doi-asserted-by":"publisher","first-page":"355","DOI":"10.1111\/1475-6803.00063","article-title":"The effect of stock splits on liquidity and excess returns: evidence from shareholder ownership composition","volume":"26","author":"Dennis","year":"2003","journal-title":"J Financ Res"},{"journal-title":"Comparative Liquidity Advantages among Major U.S. Stock Markets.","year":"1984","author":"Hui","key":"B4"},{"key":"B5","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1016\/S1386-4181(01)00024-6","article-title":"Illiquidity and stock returns: cross-section and time-series effects","volume":"5","author":"Amihud","year":"2002","journal-title":"J Financ Mark"},{"key":"B6","doi-asserted-by":"publisher","first-page":"10","DOI":"10.3905\/jpm.1988.409160","article-title":"Liquidity and execution costs in equity markets","volume":"14","author":"Hasbrouck","year":"1988","journal-title":"J Portfolio Manag"},{"key":"B7","doi-asserted-by":"publisher","first-page":"667780","DOI":"10.3389\/frai.2021.667780","article-title":"Forecasting quoted depth with the limit order book","volume":"4","author":"Libman","year":"2021","journal-title":"Front Artif Intell"},{"volume-title":"Fractal Market Analysis \u2014 Applying Chaos Theory to Investment and Analysis","year":"1994","author":"Peters","key":"B8"},{"key":"B9","doi-asserted-by":"publisher","first-page":"1250065","DOI":"10.1142\/S0219525912500658","article-title":"Fractal markets hypothesis and the global financial crisis: scaling, investment horizons and liquidity","volume":"15","author":"Kristoufek","year":"2012","journal-title":"Adv Complex Syst"},{"key":"B10","doi-asserted-by":"publisher","first-page":"144","DOI":"10.1016\/j.physa.2014.03.073","article-title":"Fractal markets: liquidity and investors on different time horizons","volume":"407","author":"Li","year":"2014","journal-title":"Phys A: Stat Mech Appl"},{"key":"B11","article-title":"The Fractal Market Hypothesis and its implications for the stability of financial markets","author":"Anderson","year":"2013","journal-title":"Bank of England, Financial Stability Paper n23"},{"key":"B12","doi-asserted-by":"publisher","first-page":"117","DOI":"10.3390\/math10010117","article-title":"A review of the fractal market hypothesis for trading and market price prediction","volume":"10","author":"Blackledge","year":"2022","journal-title":"Mathematics"},{"key":"B13","doi-asserted-by":"publisher","first-page":"1950001","DOI":"10.1142\/S2010495219500015","article-title":"Investment implications of the fractal market. 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