{"id":"https://openalex.org/W4414268345","doi":"https://doi.org/10.3390/e27090955","title":"Entropy and Chaos-Based Modeling of Nonlinear Dependencies in Commodity Markets","display_name":"Entropy and Chaos-Based Modeling of Nonlinear Dependencies in Commodity Markets","publication_year":2025,"publication_date":"2025-09-14","ids":{"openalex":"https://openalex.org/W4414268345","doi":"https://doi.org/10.3390/e27090955","pmid":"https://pubmed.ncbi.nlm.nih.gov/41008081"},"language":"en","primary_location":{"id":"doi:10.3390/e27090955","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e27090955","pdf_url":"https://www.mdpi.com/1099-4300/27/9/955/pdf?version=1757934081","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/27/9/955/pdf?version=1757934081","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014427304","display_name":"Irina Georgescu","orcid":"https://orcid.org/0000-0002-8536-5636"},"institutions":[{"id":"https://openalex.org/I88491126","display_name":"Bucharest University of Economic Studies","ror":"https://ror.org/04yvncj21","country_code":"RO","type":"education","lineage":["https://openalex.org/I88491126"]}],"countries":["RO"],"is_corresponding":true,"raw_author_name":"Irina Georgescu","raw_affiliation_strings":["Department of Economic Informatics and Cybernetics, Bucharest University of Economics, Calea Doroban\u021bi, 010552 Bucharest, Romania"],"raw_orcid":"https://orcid.org/0000-0002-8536-5636","affiliations":[{"raw_affiliation_string":"Department of Economic Informatics and Cybernetics, Bucharest University of Economics, Calea Doroban\u021bi, 010552 Bucharest, Romania","institution_ids":["https://openalex.org/I88491126"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020175868","display_name":"Jani Kinnunen","orcid":"https://orcid.org/0000-0002-0154-6617"},"institutions":[{"id":"https://openalex.org/I63548447","display_name":"Lappeenranta-Lahti University of Technology","ror":"https://ror.org/0208vgz68","country_code":"FI","type":"education","lineage":["https://openalex.org/I63548447"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Jani Kinnunen","raw_affiliation_strings":["School of Business, LUT University, Yliopistonkatu 34, 53851 Lappeenranta, Finland"],"raw_orcid":"https://orcid.org/0000-0002-0154-6617","affiliations":[{"raw_affiliation_string":"School of Business, LUT University, Yliopistonkatu 34, 53851 Lappeenranta, Finland","institution_ids":["https://openalex.org/I63548447"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5014427304"],"corresponding_institution_ids":["https://openalex.org/I88491126"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":5.1188,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.95501007,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"27","issue":"9","first_page":"955","last_page":"955"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.9947999715805054,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.9947999715805054,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11059","display_name":"Market Dynamics and Volatility","score":0.9865000247955322,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9210000038146973,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6248000264167786},{"id":"https://openalex.org/keywords/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.5394999980926514},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.49470001459121704},{"id":"https://openalex.org/keywords/portfolio","display_name":"Portfolio","score":0.4580000042915344},{"id":"https://openalex.org/keywords/coherence","display_name":"Coherence (philosophical gambling strategy)","score":0.4519999921321869},{"id":"https://openalex.org/keywords/diversification","display_name":"Diversification (marketing strategy)","score":0.4388999938964844},{"id":"https://openalex.org/keywords/commodity","display_name":"Commodity","score":0.4318000078201294},{"id":"https://openalex.org/keywords/transfer-entropy","display_name":"Transfer entropy","score":0.38999998569488525},{"id":"https://openalex.org/keywords/autocorrelation","display_name":"Autocorrelation","score":0.38600000739097595},{"id":"https://openalex.org/keywords/chaos-theory","display_name":"Chaos theory","score":0.37549999356269836}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6248000264167786},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.5394999980926514},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.5056999921798706},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.49470001459121704},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4765999913215637},{"id":"https://openalex.org/C2780821815","wikidata":"https://www.wikidata.org/wiki/Q5340806","display_name":"Portfolio","level":2,"score":0.4580000042915344},{"id":"https://openalex.org/C2781181686","wikidata":"https://www.wikidata.org/wiki/Q4226068","display_name":"Coherence (philosophical gambling strategy)","level":2,"score":0.4519999921321869},{"id":"https://openalex.org/C180916674","wikidata":"https://www.wikidata.org/wiki/Q3711935","display_name":"Diversification (marketing strategy)","level":2,"score":0.4388999938964844},{"id":"https://openalex.org/C2779439359","wikidata":"https://www.wikidata.org/wiki/Q317088","display_name":"Commodity","level":2,"score":0.4318000078201294},{"id":"https://openalex.org/C182049051","wikidata":"https://www.wikidata.org/wiki/Q17147155","display_name":"Transfer entropy","level":3,"score":0.38999998569488525},{"id":"https://openalex.org/C5297727","wikidata":"https://www.wikidata.org/wiki/Q786970","display_name":"Autocorrelation","level":2,"score":0.38600000739097595},{"id":"https://openalex.org/C92866567","wikidata":"https://www.wikidata.org/wiki/Q166314","display_name":"Chaos theory","level":3,"score":0.37549999356269836},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.3747999966144562},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.3718999922275543},{"id":"https://openalex.org/C185874996","wikidata":"https://www.wikidata.org/wiki/Q269699","display_name":"Interdependence","level":2,"score":0.3711000084877014},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3628999888896942},{"id":"https://openalex.org/C106752470","wikidata":"https://www.wikidata.org/wiki/Q1364826","display_name":"Joint entropy","level":3,"score":0.3425999879837036},{"id":"https://openalex.org/C2776667075","wikidata":"https://www.wikidata.org/wiki/Q2922469","display_name":"Commodity market","level":2,"score":0.32499998807907104},{"id":"https://openalex.org/C2780299701","wikidata":"https://www.wikidata.org/wiki/Q475000","display_name":"Stock market","level":3,"score":0.3018999993801117},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.29409998655319214},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.2858999967575073},{"id":"https://openalex.org/C152139883","wikidata":"https://www.wikidata.org/wiki/Q252973","display_name":"Mutual information","level":2,"score":0.28459998965263367},{"id":"https://openalex.org/C109510780","wikidata":"https://www.wikidata.org/wiki/Q17149502","display_name":"Total correlation","level":3,"score":0.2775000035762787},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.2773999869823456},{"id":"https://openalex.org/C9725762","wikidata":"https://www.wikidata.org/wiki/Q1072885","display_name":"Modern portfolio theory","level":3,"score":0.27230000495910645},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.2621999979019165},{"id":"https://openalex.org/C106306483","wikidata":"https://www.wikidata.org/wiki/Q183984","display_name":"Futures contract","level":2,"score":0.2558000087738037},{"id":"https://openalex.org/C110601934","wikidata":"https://www.wikidata.org/wiki/Q5172849","display_name":"Correlation dimension","level":4,"score":0.25440001487731934},{"id":"https://openalex.org/C151406439","wikidata":"https://www.wikidata.org/wiki/Q186588","display_name":"Time series","level":2,"score":0.25369998812675476},{"id":"https://openalex.org/C196216189","wikidata":"https://www.wikidata.org/wiki/Q2867","display_name":"Wavelet transform","level":3,"score":0.2515999972820282},{"id":"https://openalex.org/C19244329","wikidata":"https://www.wikidata.org/wiki/Q208697","display_name":"Financial market","level":2,"score":0.2506999969482422}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e27090955","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e27090955","pdf_url":"https://www.mdpi.com/1099-4300/27/9/955/pdf?version=1757934081","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmid:41008081","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/41008081","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:doaj.org/article:7e5adc20fbb645eda806e2e90925ef60","is_oa":true,"landing_page_url":"https://doaj.org/article/7e5adc20fbb645eda806e2e90925ef60","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 27, Iss 9, p 955 (2025)","raw_type":"article"},{"id":"pmh:oai:europepmc.org:11276587","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/12468453","pdf_url":null,"source":{"id":"https://openalex.org/S4306400806","display_name":"Europe PMC (PubMed Central)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1303153112","host_organization_name":"European Bioinformatics Institute","host_organization_lineage":["https://openalex.org/I1303153112"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:12468453","is_oa":true,"landing_page_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC12468453/","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e27090955","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e27090955","pdf_url":"https://www.mdpi.com/1099-4300/27/9/955/pdf?version=1757934081","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4414268345.pdf","grobid_xml":"https://content.openalex.org/works/W4414268345.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W122965473","https://openalex.org/W1987203652","https://openalex.org/W1990475559","https://openalex.org/W1995875735","https://openalex.org/W2029401646","https://openalex.org/W2031365860","https://openalex.org/W2034139177","https://openalex.org/W2040704490","https://openalex.org/W2047286795","https://openalex.org/W2067351362","https://openalex.org/W2092939357","https://openalex.org/W2124459709","https://openalex.org/W2173306896","https://openalex.org/W2492703958","https://openalex.org/W2888174812","https://openalex.org/W3119059523","https://openalex.org/W3148222858","https://openalex.org/W3179138095","https://openalex.org/W4283816390","https://openalex.org/W4286640307","https://openalex.org/W4299429830","https://openalex.org/W4300059230","https://openalex.org/W4307511731","https://openalex.org/W4377294238","https://openalex.org/W4396657602","https://openalex.org/W4401170291","https://openalex.org/W4402747271","https://openalex.org/W4403835724","https://openalex.org/W4406461661","https://openalex.org/W4410006316","https://openalex.org/W4411344522"],"related_works":[],"abstract_inverted_index":{"This":[0],"study":[1],"explores":[2],"the":[3,51,91],"nonlinear":[4,79],"dynamics":[5,103],"and":[6,15,21,42,45,61,77,86,101,113],"interdependencies":[7],"among":[8,82],"major":[9],"commodity":[10,105],"markets-Gold,":[11],"Oil,":[12],"Natural":[13],"Gas,":[14],"Silver-by":[16],"employing":[17],"advanced":[18],"chaos":[19,76],"theory":[20],"information-theoretic":[22],"tools.":[23],"Using":[24],"daily":[25],"data":[26],"from":[27],"2020":[28],"to":[29,57,65,97],"2024,":[30],"we":[31],"estimate":[32],"key":[33],"complexity":[34],"measures":[35],"including":[36],"Lyapunov":[37],"exponents,":[38],"correlation":[39],"dimension,":[40],"Shannon":[41],"R\u00e9nyi":[43],"entropy,":[44],"mutual":[46],"information.":[47],"We":[48],"also":[49],"apply":[50],"stochastic":[52],"SO(2)":[53],"Lie":[54],"group":[55],"method":[56],"model":[58],"dynamic":[59],"correlations,":[60],"wavelet":[62],"coherence":[63],"analysis":[64],"detect":[66],"time-frequency":[67],"co-movements.":[68],"Our":[69],"findings":[70],"reveal":[71],"evidence":[72],"of":[73,93],"low-dimensional":[74],"deterministic":[75],"time-varying":[78],"relationships,":[80],"especially":[81],"pairs":[83],"like":[84],"Gold-Silver":[85],"Oil-Gas.":[87],"These":[88],"results":[89],"highlight":[90],"importance":[92],"using":[94],"nontraditional":[95],"approaches":[96],"uncover":[98],"hidden":[99],"structure":[100],"co-movement":[102],"in":[104],"markets,":[106],"providing":[107],"useful":[108],"insights":[109],"for":[110],"portfolio":[111],"diversification":[112],"systemic":[114],"risk":[115],"assessment.":[116]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
