{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T14:32:46Z","timestamp":1782916366865,"version":"3.54.5"},"reference-count":69,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2020,1,6]],"date-time":"2020-01-06T00:00:00Z","timestamp":1578268800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["71661002"],"award-info":[{"award-number":["71661002"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["41671532"],"award-info":[{"award-number":["41671532"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["2016M592605"],"award-info":[{"award-number":["2016M592605"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>How different are the emerging and the well-developed stock markets in terms of efficiency? To gain insights into this question, we compared an important emerging market, the Chinese stock market, and the largest and the most developed market, the US stock market. Specifically, we computed the Lempel\u2013Ziv complexity (LZ) and the permutation entropy (PE) from two composite stock indices, the Shanghai stock exchange composite index (SSE) and the Dow Jones industrial average (DJIA), for both low-frequency (daily) and high-frequency (minute-to-minute)stock index data. We found that the US market is basically fully random and consistent with efficient market hypothesis (EMH), irrespective of whether low- or high-frequency stock index data are used. The Chinese market is also largely consistent with the EMH when low-frequency data are used. However, a completely different picture emerges when the high-frequency stock index data are used, irrespective of whether the LZ or PE is computed. In particular, the PE decreases substantially in two significant time windows, each encompassing a rapid market rise and then a few gigantic stock crashes. To gain further insights into the causes of the difference in the complexity changes in the two markets, we computed the Hurst parameter H from the high-frequency stock index data of the two markets and examined their temporal variations. We found that in stark contrast with the US market, whose H is always close to 1\/2, which indicates fully random behavior, for the Chinese market, H deviates from 1\/2 significantly for time scales up to about 10 min within a day, and varies systemically similar to the PE for time scales from about 10 min to a day. This opens the door for large-scale collective behavior to occur in the Chinese market, including herding behavior and large-scale manipulation as a result of inside information.<\/jats:p>","DOI":"10.3390\/e22010075","type":"journal-article","created":{"date-parts":[[2020,1,6]],"date-time":"2020-01-06T10:34:46Z","timestamp":1578306886000},"page":"75","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["Complexity Changes in the US and China\u2019s Stock Markets: Differences, Causes, and Wider Social Implications"],"prefix":"10.3390","volume":"22","author":[{"given":"Jianbo","family":"Gao","sequence":"first","affiliation":[{"name":"Center for Geodata and Analysis, Faculty of Geographical Science, Beijing Normal University, Beijing 100875, China"},{"name":"Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"International College, Guangxi University, Nanning 530004, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2933-738X","authenticated-orcid":false,"given":"Yunfei","family":"Hou","sequence":"additional","affiliation":[{"name":"School of Economics and Management, Wuhan University, Wuhan 430072, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fangli","family":"Fan","sequence":"additional","affiliation":[{"name":"Center for Geodata and Analysis, Faculty of Geographical Science, Beijing Normal University, Beijing 100875, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9435-9353","authenticated-orcid":false,"given":"Feiyan","family":"Liu","sequence":"additional","affiliation":[{"name":"International College, Guangxi University, Nanning 530004, China"},{"name":"CityDO, Hangzhou 310000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,1,6]]},"reference":[{"key":"ref_1","first-page":"41","article-title":"Proof that properly anticipated prices fluctuate randomly","volume":"6","author":"Samuelson","year":"1965","journal-title":"Ind. 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