{"id":"https://openalex.org/W1986500685","doi":"https://doi.org/10.1142/s0129183105007972","title":"SELF-SIMILAR LOG-PERIODIC STRUCTURES IN WESTERN STOCK MARKETS FROM 2000","display_name":"SELF-SIMILAR LOG-PERIODIC STRUCTURES IN WESTERN STOCK MARKETS FROM 2000","publication_year":2005,"publication_date":"2005-09-01","ids":{"openalex":"https://openalex.org/W1986500685","doi":"https://doi.org/10.1142/s0129183105007972","mag":"1986500685"},"language":"en","primary_location":{"id":"doi:10.1142/s0129183105007972","doi":"https://doi.org/10.1142/s0129183105007972","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129183105007972","pdf_url":null,"source":{"id":"https://openalex.org/S142835798","display_name":"International Journal of Modern Physics C","issn_l":"0129-1831","issn":["0129-1831","1793-6586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","jufo-1","norway-1","poland-40","russia-white-list-3"],"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Modern Physics C","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/cond-mat/0501513","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"M. BARTOLOZZI","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I5681781","display_name":"The University of Adelaide","ror":"https://ror.org/00892tw58","country_code":"AU","type":"education","lineage":["https://openalex.org/I4405259444","https://openalex.org/I5681781"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"M. BARTOLOZZI","raw_affiliation_strings":["Special Research Centre for the Subatomic Structure of Matter (CSSM), University of Adelaide, Adelaide, SA 5005, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Special Research Centre for the Subatomic Structure of Matter (CSSM), University of Adelaide, Adelaide, SA 5005, Australia","institution_ids":["https://openalex.org/I5681781"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033551127","display_name":"Stanis\u0142aw Dro\u017cd\u017c","orcid":"https://orcid.org/0000-0003-1613-6175","observed_orcids":["https://orcid.org/0000-0003-1613-6175"]},"institutions":[{"id":"https://openalex.org/I4210106918","display_name":"Institute of Nuclear Physics, Polish Academy of Sciences","ror":"https://ror.org/01n78t774","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210106918","https://openalex.org/I99542240"]},{"id":"https://openalex.org/I98559091","display_name":"University of Rzesz\u00f3w","ror":"https://ror.org/03pfsnq21","country_code":"PL","type":"education","lineage":["https://openalex.org/I98559091"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"S. DRO\u017bD\u017b","raw_affiliation_strings":["Institute of Nuclear Physics, Radzikowskiego 152, 31\u2013342 Krak\u00f3w, Poland","Institute of Physics, University of Rzesz\u00f3w, PL-35-310 Rzesz\u00f3w, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Nuclear Physics, Radzikowskiego 152, 31\u2013342 Krak\u00f3w, Poland","institution_ids":["https://openalex.org/I4210106918"]},{"raw_affiliation_string":"Institute of Physics, University of Rzesz\u00f3w, PL-35-310 Rzesz\u00f3w, Poland","institution_ids":["https://openalex.org/I98559091"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035113414","display_name":"Derek B. Leinweber","orcid":"https://orcid.org/0000-0002-4745-6027","observed_orcids":["https://orcid.org/0000-0002-4745-6027"]},"institutions":[{"id":"https://openalex.org/I5681781","display_name":"The University of Adelaide","ror":"https://ror.org/00892tw58","country_code":"AU","type":"education","lineage":["https://openalex.org/I4405259444","https://openalex.org/I5681781"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"D. B. LEINWEBER","raw_affiliation_strings":["Special Research Centre for the Subatomic Structure of Matter (CSSM), University of Adelaide, Adelaide, SA 5005, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Special Research Centre for the Subatomic Structure of Matter (CSSM), University of Adelaide, Adelaide, SA 5005, Australia","institution_ids":["https://openalex.org/I5681781"]}]},{"author_position":"middle","author":{"id":null,"display_name":"J. SPETH","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I171892758","display_name":"Forschungszentrum J\u00fclich","ror":"https://ror.org/02nv7yv05","country_code":"DE","type":"facility","lineage":["https://openalex.org/I1305996414","https://openalex.org/I171892758"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"J. SPETH","raw_affiliation_strings":["Institute f\u00fcr Kernphysik, Forschungszentrum J\u00fclich, D\u201352425 J\u00fclich, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute f\u00fcr Kernphysik, Forschungszentrum J\u00fclich, D\u201352425 J\u00fclich, Germany","institution_ids":["https://openalex.org/I171892758"]}]},{"author_position":"last","author":{"id":null,"display_name":"A. W. THOMAS","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I29801172","display_name":"Thomas Jefferson National Accelerator Facility","ror":"https://ror.org/02vwzrd76","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I29801172","https://openalex.org/I39565521"]},{"id":"https://openalex.org/I5681781","display_name":"The University of Adelaide","ror":"https://ror.org/00892tw58","country_code":"AU","type":"education","lineage":["https://openalex.org/I4405259444","https://openalex.org/I5681781"]}],"countries":["AU","US"],"is_corresponding":false,"raw_author_name":"A. W. THOMAS","raw_affiliation_strings":["Jefferson Laboratory, 12000 Jefferson Ave., Newport News, VA 23606, USA","Special Research Centre for the Subatomic Structure of Matter (CSSM), University of Adelaide, Adelaide, SA 5005, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Jefferson Laboratory, 12000 Jefferson Ave., Newport News, VA 23606, USA","institution_ids":["https://openalex.org/I29801172"]},{"raw_affiliation_string":"Special Research Centre for the Subatomic Structure of Matter (CSSM), University of Adelaide, Adelaide, SA 5005, Australia","institution_ids":["https://openalex.org/I5681781"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.8035,"has_fulltext":true,"cited_by_count":50,"citation_normalized_percentile":{"value":0.93035292,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":87,"max":98},"biblio":{"volume":"16","issue":"09","first_page":"1347","last_page":"1361"},"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":0.9976000189781189,"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":0.9976000189781189,"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/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.00039999998989515007,"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/T12261","display_name":"Statistical Mechanics and Entropy","score":0.00039999998989515007,"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/log-periodic-oscillations","display_name":"log-periodic oscillations","score":0.9129999876022339},{"id":"https://openalex.org/keywords/self-similarity","display_name":"self-similarity","score":0.9160000085830688},{"id":"https://openalex.org/keywords/discrete-scale-invariance","display_name":"discrete scale invariance","score":0.8840000033378601},{"id":"https://openalex.org/keywords/stock-market-crash","display_name":"stock market crash","score":0.9589999914169312},{"id":"https://openalex.org/keywords/fractal-market-hypothesis","display_name":"fractal market hypothesis","score":0.699999988079071},{"id":"https://openalex.org/keywords/weierstrass-function","display_name":"Weierstrass function","score":0.902999997138977},{"id":"https://openalex.org/keywords/dax","display_name":"DAX","score":0.8960000276565552},{"id":"https://openalex.org/keywords/nasdaq-100","display_name":"NASDAQ 100","score":0.9700000286102295},{"id":"https://openalex.org/keywords/s-p-500","display_name":"S&P 500","score":1.0},{"id":"https://openalex.org/keywords/dow-jones-industrial-average","display_name":"Dow Jones Industrial Average","score":0.9760000109672546},{"id":"https://openalex.org/keywords/harmonics","display_name":"harmonics","score":0.5509999990463257}],"concepts":[{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.75},{"id":"https://openalex.org/C204036174","wikidata":"https://www.wikidata.org/wiki/Q909380","display_name":"Stock (firearms)","level":2,"score":0.6287999749183655},{"id":"https://openalex.org/C135593079","wikidata":"https://www.wikidata.org/wiki/Q1750766","display_name":"Scale invariance","level":2,"score":0.5960000157356262},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.5849999785423279},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.5659000277519226},{"id":"https://openalex.org/C2780299701","wikidata":"https://www.wikidata.org/wiki/Q475000","display_name":"Stock market","level":3,"score":0.4700999855995178},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.4643999934196472},{"id":"https://openalex.org/C188414643","wikidata":"https://www.wikidata.org/wiki/Q3001183","display_name":"Harmonics","level":3,"score":0.46070000529289246},{"id":"https://openalex.org/C162494671","wikidata":"https://www.wikidata.org/wiki/Q2845227","display_name":"Fractal analysis","level":4,"score":0.35019999742507935},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3479999899864197},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3425000011920929},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.3391999900341034},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.33489999175071716},{"id":"https://openalex.org/C2983668108","wikidata":"https://www.wikidata.org/wiki/Q280453","display_name":"Spectral analysis","level":3,"score":0.3276999890804291},{"id":"https://openalex.org/C168110828","wikidata":"https://www.wikidata.org/wiki/Q1331626","display_name":"Spectral density","level":2,"score":0.31459999084472656},{"id":"https://openalex.org/C3018587665","wikidata":"https://www.wikidata.org/wiki/Q7268696","display_name":"Qualitative analysis","level":3,"score":0.3098999857902527},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.303600013256073},{"id":"https://openalex.org/C94617000","wikidata":"https://www.wikidata.org/wiki/Q639854","display_name":"Qualitative comparative analysis","level":2,"score":0.27709999680519104},{"id":"https://openalex.org/C155739000","wikidata":"https://www.wikidata.org/wiki/Q877707","display_name":"Market structure","level":2,"score":0.2685999870300293},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25949999690055847}],"mesh":[],"locations_count":9,"locations":[{"id":"doi:10.1142/s0129183105007972","doi":"https://doi.org/10.1142/s0129183105007972","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129183105007972","pdf_url":null,"source":{"id":"https://openalex.org/S142835798","display_name":"International Journal of Modern Physics C","issn_l":"0129-1831","issn":["0129-1831","1793-6586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","jufo-1","norway-1","poland-40","russia-white-list-3"],"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Modern Physics C","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:arx:papers:cond-mat/0501513","doi":null,"is_oa":false,"landing_page_url":"http://arxiv.org/pdf/cond-mat/0501513","pdf_url":"http://arxiv.org/pdf/cond-mat/0501513","source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"preprint"},{"id":"pmh:oai:arXiv.org:cond-mat/0501513","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/cond-mat/0501513","pdf_url":"https://arxiv.org/pdf/cond-mat/0501513","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,"listed_in":[],"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":"mag:3124686040","doi":null,"is_oa":false,"landing_page_url":"https://EconPapers.repec.org/RePEc:arx:papers:cond-mat/0501513","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"RePEc: Research Papers in Economics","raw_type":null},{"id":"pmh:oai:RePEc:wsi:ijmpcx:v:16:y:2005:i:09:n:s0129183105007972","doi":null,"is_oa":false,"landing_page_url":"http://www.worldscientific.com/doi/abs/10.1142/S0129183105007972","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"},{"id":"pmh:oai:RePEc:wsi:ijmpcx:v:16:y:2005:i:09:p:1347-1361","doi":null,"is_oa":false,"landing_page_url":"http://www.worldscinet.com/cgi-bin/details.cgi?type=html&id=pii:S0129183105007972","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"},{"id":"pmh:oai:digital.library.adelaide.edu.au:2440/17564","doi":null,"is_oa":false,"landing_page_url":"http://hdl.handle.net/2440/17564","pdf_url":null,"source":{"id":"https://openalex.org/S4306401835","display_name":"Adelaide Research & Scholarship (AR&S) (University of Adelaide)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I5681781","host_organization_name":"The University of Adelaide","host_organization_lineage":["https://openalex.org/I5681781"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://dx.doi.org/10.1142/s0129183105007972","raw_type":"Journal article"},{"id":"pmh:oai:juser.fz-juelich.de:50432","doi":null,"is_oa":false,"landing_page_url":"http://juser.fz-juelich.de/record/50432","pdf_url":null,"source":{"id":"https://openalex.org/S4306401090","display_name":"JuSER (Forschungszentrum J\u00fclich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I171892758","host_organization_name":"Forschungszentrum J\u00fclich","host_organization_lineage":["https://openalex.org/I171892758"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International journal of modern physics / C 16, 1347 - 1361 (2005). doi:10.1142/S0129183105007972","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.cond-mat/0501513","doi":"https://doi.org/10.48550/arxiv.cond-mat/0501513","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.cond-mat/0501513","pdf_url":null,"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,"listed_in":[],"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:cond-mat/0501513","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/cond-mat/0501513","pdf_url":"https://arxiv.org/pdf/cond-mat/0501513","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,"listed_in":[],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1986500685.pdf","grobid_xml":"https://content.openalex.org/works/W1986500685.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W1974137611","https://openalex.org/W1979044260","https://openalex.org/W2010453459","https://openalex.org/W2021943559","https://openalex.org/W2024659360","https://openalex.org/W2026735368","https://openalex.org/W2034498168","https://openalex.org/W2039966934","https://openalex.org/W2045291634","https://openalex.org/W2054149290","https://openalex.org/W2071481304","https://openalex.org/W2075076192","https://openalex.org/W2081082758","https://openalex.org/W2083369563","https://openalex.org/W2091103026","https://openalex.org/W2138256018","https://openalex.org/W2140962554","https://openalex.org/W2149451408","https://openalex.org/W2951029834","https://openalex.org/W3038117069","https://openalex.org/W3104582607","https://openalex.org/W3121612919","https://openalex.org/W4214518794","https://openalex.org/W4233497874"],"related_works":["https://openalex.org/W2075076192","https://openalex.org/W1448113692","https://openalex.org/W3104170549","https://openalex.org/W2806759875","https://openalex.org/W3100049127","https://openalex.org/W3148824948","https://openalex.org/W7099454736","https://openalex.org/W2054149290","https://openalex.org/W2950733125","https://openalex.org/W1605029109"],"abstract_inverted_index":{"The":[0,28,84,161],"presence":[1],"of":[2,17,31,38,56,58,87,105,132,164,175,183],"log-periodic":[3,41,103,134,137,185],"structures":[4,42],"before":[5],"and":[6,70,76,110],"after":[7],"stock":[8],"market":[9],"crashes":[10],"is":[11,91,99,123],"considered":[12],"to":[13,128,170,173],"be":[14,171],"an":[15,18],"imprint":[16],"intrinsic":[19],"discrete":[20],"scale":[21],"invariance":[22],"(DSI)":[23],"in":[24,112,120],"this":[25],"complex":[26],"system.":[27],"fractal":[29,186],"framework":[30],"the":[32,36,48,53,59,66,71,73,77,81,94,130,146,165],"theory":[33],"leaves":[34],"open":[35],"possibility":[37],"observing":[39],"self-similar":[40],"at":[43],"different":[44,89],"time":[45],"scales.":[46],"In":[47],"present":[49],"work,":[50],"we":[51],"analyze":[52],"daily":[54],"closures":[55],"four":[57],"most":[60],"important":[61],"indices":[62],"worldwide":[63],"since":[64],"2000:":[65],"DAX":[67],"for":[68,80,101],"Germany":[69],"NASDAQ-100,":[72],"S&P":[74],"500":[75],"Dow":[78],"Jones":[79],"United":[82],"States.":[83],"qualitative":[85],"behavior":[86],"these":[88],"markets":[90],"similar":[92,172],"during":[93],"temporal":[95],"frame":[96],"studied.":[97],"Evidence":[98],"found":[100,169],"decelerating":[102],"oscillations":[104,138],"duration":[106],"about":[107],"two":[108],"years":[109],"starting":[111,119],"September":[113],"2000.":[114],"Moreover,":[115],"a":[116,150,176,181,184],"nested":[117],"sub-structure":[118],"May":[121],"2002":[122],"revealed,":[124],"bringing":[125],"more":[126],"evidence":[127],"support":[129],"hypothesis":[131],"self-similar,":[133],"behavior.":[135],"Ongoing":[136],"are":[139,158],"also":[140,159],"revealed.":[141],"A":[142],"Lomb":[143],"analysis":[144],"over":[145],"aforementioned":[147],"periods":[148],"indicates":[149],"preferential":[151],"scaling":[152],"factor":[153],"\u03bb~2.":[154],"Higher":[155],"order":[156],"harmonics":[157],"present.":[160],"spectral":[162],"pattern":[163],"data":[166],"has":[167],"been":[168],"that":[174],"Weierstrass-type":[177],"function,":[178],"used":[179],"as":[180],"prototype":[182],"function.":[187]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":5}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2016-06-24T00:00:00"}