{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,5]],"date-time":"2026-09-05T05:17:46Z","timestamp":1788585466432,"version":"build-2803163510"},"reference-count":53,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2026,9,3]],"date-time":"2026-09-03T00:00:00Z","timestamp":1788393600000},"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":"crossref","award":["72574097"],"award-info":[{"award-number":["72574097"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"award":["72574097"],"award-info":[{"award-number":["72574097"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Commodity futures markets exhibit pronounced non-stationarity, nonlinearity, and multifractal characteristics that challenge traditional linear models. We employ a multiscale framework integrating four methodologies\u2014MF-DCCA, PG irreversibility index, MSWPE, and JS-divergence segmentation\u2014to analyze these features using daily closing prices for WTI crude oil, agricultural commodities (US soybeans, meal, oil, and wheat), the US dollar index, and Chinese No. 2 soybeans, spanning from 2 January 2018 to 1 October 2025, sourced from Investing.com and Matteo Iacoviello\u2019s GPR database. The analysis yields three key results. First, scale dependence varies across commodities and is shaped by supply adjustment elasticity: energy markets show scale-dependent amplification and directional sign reversals, while agricultural markets maintain near-monofractal structures. Second, multiple methods converge on a characteristic time scale of approximately 20 days, linking physical logistics rhythms with financial pricing. Third, the persistence of structural reconstruction after shocks depends on systemic penetration depth, with exogenous macroeconomic uncertainty exerting stronger and more lasting effects than market-internal events. Together, supply elasticity, physical logistics rhythms, and systemic penetration depth constitute the three fundamental determinants of nonlinear commodity futures dynamics, with implications for cross-commodity allocation, multi-horizon risk management, and geopolitical scenario analysis.<\/jats:p>","DOI":"10.3390\/e28090984","type":"journal-article","created":{"date-parts":[[2026,9,3]],"date-time":"2026-09-03T11:08:53Z","timestamp":1788433733000},"page":"984","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Multiscale Complexity and Irreversibility of Non-Stationary Time Series in Commodity Futures Markets"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-8871-7449","authenticated-orcid":false,"given":"Xia","family":"Zhao","sequence":"first","affiliation":[{"name":"Institute of Food and Strategic Reserves, Nanjing University of Finance and Economics, Nanjing 210023, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"software","vocabulary":"credit"},{"role":"validation","vocabulary":"credit"},{"role":"formal-analysis","vocabulary":"credit"},{"role":"investigation","vocabulary":"credit"},{"role":"data-curation","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"visualization","vocabulary":"credit"},{"role":"funding-acquisition","vocabulary":"credit"}]},{"given":"Kaicheng","family":"Xie","sequence":"additional","affiliation":[{"name":"Institute of Food and Strategic Reserves, Nanjing University of Finance and Economics, Nanjing 210023, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"software","vocabulary":"credit"},{"role":"validation","vocabulary":"credit"},{"role":"investigation","vocabulary":"credit"},{"role":"data-curation","vocabulary":"credit"},{"role":"visualization","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"}]}],"member":"1968","published-online":{"date-parts":[[2026,9,3]]},"reference":[{"key":"ref_1","unstructured":"Waldrop, M.M. 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