{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,23]],"date-time":"2026-10-23T21:03:25Z","timestamp":1792789405712,"version":"4.5.0"},"reference-count":60,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2022,12,24]],"date-time":"2022-12-24T00:00:00Z","timestamp":1671840000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Humanities and Social Sciences Youth Foundation of the Chinese Ministry of Education","award":["22YJCZH107"],"award-info":[{"award-number":["22YJCZH107"]}]},{"name":"Humanities and Social Sciences Youth Foundation of the Chinese Ministry of Education","award":["22FCZD03"],"award-info":[{"award-number":["22FCZD03"]}]},{"name":"Scientific Research Support Program of Xi\u2019an University of Finance and Economics","award":["22YJCZH107"],"award-info":[{"award-number":["22YJCZH107"]}]},{"name":"Scientific Research Support Program of Xi\u2019an University of Finance and Economics","award":["22FCZD03"],"award-info":[{"award-number":["22FCZD03"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In econophysics, the analysis of the return distribution of a financial asset using statistical physics methods is a long-standing and important issue. This paper systematically conducts an analysis of composite index 1 min datasets over a 17-year period (2005\u20132021) for both the Shanghai and Shenzhen stock exchanges. To reveal the differences between Chinese and mature stock markets, we precisely measure the property of the return distribution of the composite index over the time scale \u0394t, which ranges from 1 min to almost 4000 min. The main findings are as follows: (1) The return distribution presents a leptokurtic, fat-tailed, and almost symmetrical shape that is similar to that of mature markets. (2) The central part of the return distribution is described by the symmetrical L\u00e9vy \u03b1-stable process, with a stability parameter comparable with a value of about 1.4, which was extracted for the U.S. stock market. (3) The return distribution can be described well by Student\u2019s t-distribution within a wider return range than the L\u00e9vy \u03b1-stable distribution. (4) Distinctively, the stability parameter shows a potential change when \u0394t increases, and thus a crossover region at 15 &lt;\u0394t&lt; 60 min is observed. This is different from the finding in the U.S. stock market that a single value of about 1.4 holds over 1 \u2264\u0394t\u2264 1000 min. (5) The tail distribution of returns at small \u0394t decays as an asymptotic power law with an exponent of about 3, which is a widely observed value in mature markets. However, it decays exponentially when \u0394t\u2265 240 min, which is not observed in mature markets. (6) Return distributions gradually converge to a normal distribution as \u0394t increases. This observation is different from the finding of a critical \u0394t= 4 days in the U.S. stock market.<\/jats:p>","DOI":"10.3390\/e25010036","type":"journal-article","created":{"date-parts":[[2022,12,27]],"date-time":"2022-12-27T04:42:47Z","timestamp":1672116167000},"page":"36","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Precision Measurement of the Return Distribution Property of the Chinese Stock Market Index"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9115-2055","authenticated-orcid":false,"given":"Peng","family":"Liu","sequence":"first","affiliation":[{"name":"School of Information, Xi\u2019an University of Finance and Economics, Xi\u2019an 710100, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1092-072X","authenticated-orcid":false,"given":"Yanyan","family":"Zheng","sequence":"additional","affiliation":[{"name":"School of Management, Xi\u2019an Polytechnic University, Xi\u2019an 710048, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,24]]},"reference":[{"key":"ref_1","unstructured":"The Nobel Foundation (2022, December 18). 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