{"id":"https://openalex.org/W3158819298","doi":"https://doi.org/10.3390/e23060670","title":"Ordinal Pattern Dependence in the Context of Long-Range Dependence","display_name":"Ordinal Pattern Dependence in the Context of Long-Range Dependence","publication_year":2021,"publication_date":"2021-05-26","ids":{"openalex":"https://openalex.org/W3158819298","doi":"https://doi.org/10.3390/e23060670","mag":"3158819298","pmid":"https://pubmed.ncbi.nlm.nih.gov/34073336"},"language":"en","primary_location":{"id":"doi:10.3390/e23060670","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23060670","pdf_url":"https://www.mdpi.com/1099-4300/23/6/670/pdf?version=1622031080","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":["arxiv","crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/23/6/670/pdf?version=1622031080","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Ines N\u00fc\u00dfgen","orcid":null},"institutions":[{"id":"https://openalex.org/I206895457","display_name":"University of Siegen","ror":"https://ror.org/02azyry73","country_code":"DE","type":"education","lineage":["https://openalex.org/I206895457"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Ines N\u00fc\u00dfgen","raw_affiliation_strings":["Department of Mathematics, Siegen University, Walter-Flex-Stra\u00dfe 3, 57072 Siegen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Siegen University, Walter-Flex-Stra\u00dfe 3, 57072 Siegen, Germany","institution_ids":["https://openalex.org/I206895457"]}]},{"author_position":"last","author":{"id":null,"display_name":"Alexander Schnurr","orcid":null},"institutions":[{"id":"https://openalex.org/I206895457","display_name":"University of Siegen","ror":"https://ror.org/02azyry73","country_code":"DE","type":"education","lineage":["https://openalex.org/I206895457"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Alexander Schnurr","raw_affiliation_strings":["Department of Mathematics, Siegen University, Walter-Flex-Stra\u00dfe 3, 57072 Siegen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Siegen University, Walter-Flex-Stra\u00dfe 3, 57072 Siegen, Germany","institution_ids":["https://openalex.org/I206895457"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I206895457"],"apc_list":{"value":1800,"currency":"CHF","value_usd":1944},"apc_paid":{"value":1800,"currency":"CHF","value_usd":1944},"fwci":0.8779,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.75754579,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"23","issue":"6","first_page":"670","last_page":"670"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10282","display_name":"Financial Risk and Volatility Modeling","score":0.5371000170707703,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"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/T10282","display_name":"Financial Risk and Volatility Modeling","score":0.5371000170707703,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"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/T11443","display_name":"Advanced Statistical Process Monitoring","score":0.09430000185966492,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11918","display_name":"Forecasting Techniques and Applications","score":0.07079999893903732,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.6718000173568726},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.6452000141143799},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.6251999735832214},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.6146000027656555},{"id":"https://openalex.org/keywords/ordinal-regression","display_name":"Ordinal regression","score":0.5924000144004822},{"id":"https://openalex.org/keywords/ordinal-data","display_name":"Ordinal data","score":0.5713000297546387},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5325000286102295}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7235000133514404},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6718000173568726},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.6452000141143799},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.6251999735832214},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.6146000027656555},{"id":"https://openalex.org/C110313322","wikidata":"https://www.wikidata.org/wiki/Q7100793","display_name":"Ordinal regression","level":2,"score":0.5924000144004822},{"id":"https://openalex.org/C85461838","wikidata":"https://www.wikidata.org/wiki/Q7100785","display_name":"Ordinal data","level":2,"score":0.5713000297546387},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5325000286102295},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.4839000105857849},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.46399998664855957},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.44760000705718994},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.38940000534057617},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.3237000107765198},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.2892000079154968},{"id":"https://openalex.org/C88871306","wikidata":"https://www.wikidata.org/wiki/Q7208287","display_name":"Point process","level":2,"score":0.28279998898506165},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2800000011920929},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.2766999900341034},{"id":"https://openalex.org/C151406439","wikidata":"https://www.wikidata.org/wiki/Q186588","display_name":"Time series","level":2,"score":0.27469998598098755}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e23060670","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23060670","pdf_url":"https://www.mdpi.com/1099-4300/23/6/670/pdf?version=1622031080","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:34073336","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/34073336","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":"Journal Article"},{"id":"pmh:oai:arXiv.org:2105.00724","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2105.00724","pdf_url":"https://arxiv.org/pdf/2105.00724","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:pubmedcentral.nih.gov:8230352","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/8230352","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"},{"id":"pmh:oai:doaj.org/article:a6d679781b4241e0ba5d44a3f8b64bb4","is_oa":true,"landing_page_url":"https://doaj.org/article/a6d679781b4241e0ba5d44a3f8b64bb4","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 23, Iss 6, p 670 (2021)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/e23060670","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23060670","pdf_url":"https://www.mdpi.com/1099-4300/23/6/670/pdf?version=1622031080","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":[{"id":"https://openalex.org/G6160719464","display_name":null,"funder_award_id":"SCHN 1231-3/2","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3158819298.pdf"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W1508427692","https://openalex.org/W1526575354","https://openalex.org/W1555022314","https://openalex.org/W1970669268","https://openalex.org/W2014683958","https://openalex.org/W2015280347","https://openalex.org/W2025517929","https://openalex.org/W2031390992","https://openalex.org/W2039797951","https://openalex.org/W2043362214","https://openalex.org/W2049834491","https://openalex.org/W2073087000","https://openalex.org/W2107163666","https://openalex.org/W2109214436","https://openalex.org/W2167430018","https://openalex.org/W2341760625","https://openalex.org/W2612022290","https://openalex.org/W2742565288","https://openalex.org/W2963864002","https://openalex.org/W2971403412","https://openalex.org/W2997487160","https://openalex.org/W3014058384","https://openalex.org/W3037847066","https://openalex.org/W3135798417","https://openalex.org/W4229692794","https://openalex.org/W4292963524","https://openalex.org/W4312258136","https://openalex.org/W6637809935","https://openalex.org/W6657608170"],"related_works":[],"abstract_inverted_index":{"Ordinal":[0],"pattern":[1,47,72],"dependence":[2,6,37,48,91],"is":[3,27,125],"a":[4,50,122],"multivariate":[5,118],"measure":[7],"based":[8],"on":[9,35,94],"the":[10,24,36,39,65,80,85,108,115],"co-movement":[11],"of":[12,58,70,117],"two":[13,40],"time":[14,21,53,87],"series.":[15],"In":[16,74],"strong":[17],"connection":[18],"to":[19,31,127],"ordinal":[20,25,46,71],"series":[22,54,88],"analysis,":[23],"information":[26],"taken":[28],"into":[29],"account":[30],"derive":[32],"robust":[33],"results":[34],"between":[38],"processes.":[41,120],"This":[42],"article":[43],"deals":[44],"with":[45],"for":[49,68,84,107],"long-range":[51,61],"dependent":[52],"including":[55],"mixed":[56],"cases":[57],"short-":[59],"and":[60,98],"dependence.":[62,73],"We":[63],"investigate":[64],"limit":[66,100,105],"distributions":[67,106],"estimators":[69],"doing":[75],"so,":[76],"we":[77],"point":[78],"out":[79],"differences":[81],"that":[82],"arise":[83],"underlying":[86],"having":[89],"different":[90],"structures.":[92],"Depending":[93],"these":[95],"assumptions,":[96],"central":[97],"non-central":[99],"theorems":[101],"are":[102],"proven.":[103],"The":[104],"latter":[109],"ones":[110],"can":[111],"be":[112],"included":[113],"in":[114],"class":[116],"Rosenblatt":[119],"Finally,":[121],"simulation":[123],"study":[124],"provided":[126],"illustrate":[128],"our":[129],"theoretical":[130],"findings.":[131]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2026-08-28T12:50:07.497085","created_date":"2021-05-10T00:00:00"}
