{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T17:22:58Z","timestamp":1780507378729,"version":"3.54.1"},"reference-count":42,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2017,12,31]],"date-time":"2017-12-31T00:00:00Z","timestamp":1514678400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["2017M610045"],"award-info":[{"award-number":["2017M610045"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["FRF-BR-17-007A"],"award-info":[{"award-number":["FRF-BR-17-007A"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The regularity of price fluctuations in exchange rates plays a crucial role in foreign exchange (FX) market dynamics. In this paper, we quantify the multiply irregular fluctuation behaviors of exchange rates in the last 10 years (November 2006\u2013November 2016) of eight world economies with two nonlinear approaches. One is a recently proposed multiscale weighted permutation entropy (MWPE) and another is the typical quantification recurrence analysis (RQA) technique. Furthermore, we utilize the RQA technique to study the different intrinsic mode functions (IMFs) that represents different frequencies and scales of the raw time series via the empirical mode decomposition algorithm. Complexity characteristics of abundance and distinction are obtained in the foreign exchange markets. The empirical results show that JPY\/USD (followed by EUR\/USD) implies a a higher complexity and indicates relatively higher efficiency of the Japanese FX market, while some economies like South Korea, Hong Kong and China show lower and weaker efficiency of their FX markets. Meanwhile, it is suggested that the financial crisis enhances the market efficiency in the FX markets.<\/jats:p>","DOI":"10.3390\/e20010017","type":"journal-article","created":{"date-parts":[[2018,1,3]],"date-time":"2018-01-03T12:00:06Z","timestamp":1514980806000},"page":"17","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Nonlinear Multiscale Entropy and Recurrence Quantification Analysis of Foreign Exchange Markets Efficiency"],"prefix":"10.3390","volume":"20","author":[{"given":"Hongli","family":"Niu","sequence":"first","affiliation":[{"name":"Donlinks School of Economics and Management, University of Science and Technology Beijing, Beijing 100083, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lin","family":"Zhang","sequence":"additional","affiliation":[{"name":"Donlinks School of Economics and Management, University of Science and Technology Beijing, Beijing 100083, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2017,12,31]]},"reference":[{"key":"ref_1","unstructured":"Calvet, L.E., and Fisher, A.J. 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