{"id":"https://openalex.org/W3010891413","doi":"https://doi.org/10.3390/e22030330","title":"Permutation Entropy as a Measure of Information Gain/Loss in the Different Symbolic Descriptions of Financial Data","display_name":"Permutation Entropy as a Measure of Information Gain/Loss in the Different Symbolic Descriptions of Financial Data","publication_year":2020,"publication_date":"2020-03-13","ids":{"openalex":"https://openalex.org/W3010891413","doi":"https://doi.org/10.3390/e22030330","mag":"3010891413","pmid":"https://pubmed.ncbi.nlm.nih.gov/33286104"},"language":"en","primary_location":{"id":"doi:10.3390/e22030330","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e22030330","pdf_url":"https://www.mdpi.com/1099-4300/22/3/330/pdf","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/1099-4300/22/3/330/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058492651","display_name":"Jan Koz\u00e1k","orcid":"https://orcid.org/0000-0002-2128-6998"},"institutions":[{"id":"https://openalex.org/I188922065","display_name":"University of Economics in Katowice","ror":"https://ror.org/01vxt3d40","country_code":"PL","type":"education","lineage":["https://openalex.org/I188922065"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Jan Kozak","raw_affiliation_strings":["Faculty of Informatics and Communication; Department of Knowledge Engineering, University of Economics, 1 Maja 50, 40-287 Katowice, Poland","Faculty of Informatics and Communication"],"raw_orcid":"https://orcid.org/0000-0002-2128-6998","affiliations":[{"raw_affiliation_string":"Faculty of Informatics and Communication; Department of Knowledge Engineering, University of Economics, 1 Maja 50, 40-287 Katowice, Poland","institution_ids":["https://openalex.org/I188922065"]},{"raw_affiliation_string":"Faculty of Informatics and Communication","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091059693","display_name":"Krzysztof Kania","orcid":"https://orcid.org/0000-0002-7123-6972"},"institutions":[{"id":"https://openalex.org/I188922065","display_name":"University of Economics in Katowice","ror":"https://ror.org/01vxt3d40","country_code":"PL","type":"education","lineage":["https://openalex.org/I188922065"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Krzysztof Kania","raw_affiliation_strings":["Faculty of Informatics and Communication; Department of Knowledge Engineering, University of Economics, 1 Maja 50, 40-287 Katowice, Poland","Faculty of Informatics and Communication"],"raw_orcid":"https://orcid.org/0000-0002-7123-6972","affiliations":[{"raw_affiliation_string":"Faculty of Informatics and Communication; Department of Knowledge Engineering, University of Economics, 1 Maja 50, 40-287 Katowice, Poland","institution_ids":["https://openalex.org/I188922065"]},{"raw_affiliation_string":"Faculty of Informatics and Communication","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004266128","display_name":"Przemys\u0142aw Juszczuk","orcid":"https://orcid.org/0000-0001-7893-5410"},"institutions":[{"id":"https://openalex.org/I188922065","display_name":"University of Economics in Katowice","ror":"https://ror.org/01vxt3d40","country_code":"PL","type":"education","lineage":["https://openalex.org/I188922065"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Przemys\u0142aw Juszczuk","raw_affiliation_strings":["Faculty of Informatics and Communication; Department of Knowledge Engineering, University of Economics, 1 Maja 50, 40-287 Katowice, Poland","Faculty of Informatics and Communication"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Informatics and Communication; Department of Knowledge Engineering, University of Economics, 1 Maja 50, 40-287 Katowice, Poland","institution_ids":["https://openalex.org/I188922065"]},{"raw_affiliation_string":"Faculty of Informatics and Communication","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5058492651"],"corresponding_institution_ids":["https://openalex.org/I188922065"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":2.4843,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.92892259,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"22","issue":"3","first_page":"330","last_page":"330"},"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":0.9983999729156494,"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":0.9983999729156494,"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":0.9776999950408936,"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"}},{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9690999984741211,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.6324827671051025},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5672138333320618},{"id":"https://openalex.org/keywords/volatility","display_name":"Volatility (finance)","score":0.501471996307373},{"id":"https://openalex.org/keywords/transfer-entropy","display_name":"Transfer entropy","score":0.4950949251651764},{"id":"https://openalex.org/keywords/financial-market","display_name":"Financial market","score":0.43633562326431274},{"id":"https://openalex.org/keywords/information-theory","display_name":"Information theory","score":0.4255140721797943},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.39933574199676514},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.3787016272544861},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.34112367033958435},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.33946913480758667},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2599540650844574},{"id":"https://openalex.org/keywords/finance","display_name":"Finance","score":0.2517111301422119},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.20885774493217468},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.20529869198799133},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.12254256010055542}],"concepts":[{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.6324827671051025},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5672138333320618},{"id":"https://openalex.org/C91602232","wikidata":"https://www.wikidata.org/wiki/Q756115","display_name":"Volatility (finance)","level":2,"score":0.501471996307373},{"id":"https://openalex.org/C182049051","wikidata":"https://www.wikidata.org/wiki/Q17147155","display_name":"Transfer entropy","level":3,"score":0.4950949251651764},{"id":"https://openalex.org/C19244329","wikidata":"https://www.wikidata.org/wiki/Q208697","display_name":"Financial market","level":2,"score":0.43633562326431274},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.4255140721797943},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.39933574199676514},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.3787016272544861},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34112367033958435},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.33946913480758667},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2599540650844574},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.2517111301422119},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.20885774493217468},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.20529869198799133},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.12254256010055542},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e22030330","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e22030330","pdf_url":"https://www.mdpi.com/1099-4300/22/3/330/pdf","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:33286104","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33286104","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:d1e7be704212415da1ddf83d66702572","is_oa":true,"landing_page_url":"https://doaj.org/article/d1e7be704212415da1ddf83d66702572","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 22, Iss 3, p 330 (2020)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/22/3/330/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/e22030330","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"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","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:7516788","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7516788","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/e22030330","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e22030330","pdf_url":"https://www.mdpi.com/1099-4300/22/3/330/pdf","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":[{"display_name":"Peace, Justice and strong institutions","score":0.6499999761581421,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3010891413.pdf","grobid_xml":"https://content.openalex.org/works/W3010891413.grobid-xml"},"referenced_works_count":44,"referenced_works":["https://openalex.org/W1259078","https://openalex.org/W1998017597","https://openalex.org/W2003618976","https://openalex.org/W2014683958","https://openalex.org/W2017148193","https://openalex.org/W2018876117","https://openalex.org/W2029526035","https://openalex.org/W2059042317","https://openalex.org/W2078764315","https://openalex.org/W2083459765","https://openalex.org/W2086712186","https://openalex.org/W2095067567","https://openalex.org/W2095738857","https://openalex.org/W2097441037","https://openalex.org/W2105499812","https://openalex.org/W2108131557","https://openalex.org/W2141514928","https://openalex.org/W2157881370","https://openalex.org/W2176118516","https://openalex.org/W2178677884","https://openalex.org/W2195027038","https://openalex.org/W2497802512","https://openalex.org/W2560316287","https://openalex.org/W2587781392","https://openalex.org/W2604113470","https://openalex.org/W2605963541","https://openalex.org/W2618121566","https://openalex.org/W2801103224","https://openalex.org/W2821173763","https://openalex.org/W2886065092","https://openalex.org/W2894466258","https://openalex.org/W2906814512","https://openalex.org/W2921342325","https://openalex.org/W2939518482","https://openalex.org/W2945095272","https://openalex.org/W2947210053","https://openalex.org/W2949687910","https://openalex.org/W2962834598","https://openalex.org/W3121465995","https://openalex.org/W4300336601","https://openalex.org/W6657892999","https://openalex.org/W6674435425","https://openalex.org/W6754004010","https://openalex.org/W6807091881"],"related_works":["https://openalex.org/W1999409691","https://openalex.org/W3105581519","https://openalex.org/W1966203994","https://openalex.org/W3032013634","https://openalex.org/W2492100837","https://openalex.org/W2061278088","https://openalex.org/W2075237332","https://openalex.org/W1595266364","https://openalex.org/W1972053074","https://openalex.org/W2055254734"],"abstract_inverted_index":{"Financial":[0],"markets":[1,28],"give":[2],"a":[3,30,99,111],"large":[4],"number":[5],"of":[6,75,84,95,101,135,144,164],"trading":[7],"opportunities.":[8],"However,":[9,52],"over-complicated":[10],"systems":[11],"make":[12],"it":[13],"very":[14],"difficult":[15],"to":[16,32,67],"be":[17],"effectively":[18],"used":[19,148],"by":[20],"decision-makers.":[21,40],"Volatility":[22],"and":[23,47,109,126,154],"noise":[24],"present":[25],"in":[26,44,133,149],"the":[27,34,39,54,60,69,73,81,88,93,102,106,141,150,155,161,165,171],"evoke":[29],"need":[31],"simplify":[33],"market":[35,61],"picture":[36],"derived":[37,86],"for":[38,87,105],"Symbolic":[41],"representation":[42,79,132],"fits":[43],"this":[45],"concept":[46],"greatly":[48],"reduces":[49],"data":[50,78,131,139],"complexity.":[51],"at":[53],"same":[55],"time,":[56],"some":[57],"information":[58,85,103],"from":[59],"is":[62,66,72],"lost.":[63],"Our":[64],"motivation":[65],"answer":[68],"question:":[70],"What":[71],"impact":[74],"introducing":[76],"different":[77,123],"on":[80,92],"overall":[82],"amount":[83],"decision-maker?":[89],"We":[90,121],"concentrate":[91],"possibility":[94],"using":[96],"entropy":[97,117,173],"as":[98,110],"measure":[100],"gain/loss":[104],"financial":[107],"data,":[108],"basic":[112],"form,":[113],"we":[114],"assume":[115],"permutation":[116,172],"with":[118,129],"later":[119],"modifications.":[120],"investigate":[122],"symbolic":[124,162],"representations":[125],"compare":[127],"them":[128],"classical":[130],"terms":[134],"entropy.":[136],"The":[137,152],"real-world":[138],"covering":[140],"time":[142,166],"span":[143],"10":[145],"years":[146],"are":[147],"experiments.":[151],"results":[153],"statistical":[156],"verification":[157],"show":[158],"that":[159],"extending":[160],"description":[163],"series":[167],"does":[168],"not":[169],"affect":[170],"values.":[174]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
