{"id":"https://openalex.org/W1970987932","doi":"https://doi.org/10.1142/s0218127414500412","title":"Correlation Dimension of Fractional Gaussian Noise: New Evidence from Wavelets","display_name":"Correlation Dimension of Fractional Gaussian Noise: New Evidence from Wavelets","publication_year":2014,"publication_date":"2014-04-01","ids":{"openalex":"https://openalex.org/W1970987932","doi":"https://doi.org/10.1142/s0218127414500412","mag":"1970987932"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127414500412","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127414500412","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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 Bifurcation and Chaos","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040771882","display_name":"Zouhaier Dhifaoui","orcid":"https://orcid.org/0000-0003-2766-1231"},"institutions":[{"id":"https://openalex.org/I8636806","display_name":"University of Sousse","ror":"https://ror.org/00dmpgj58","country_code":"TN","type":"education","lineage":["https://openalex.org/I8636806"]}],"countries":["TN"],"is_corresponding":false,"raw_author_name":"Zouhaier Dhifaoui","raw_affiliation_strings":["Higher Institute of Management, University of Sousse, Abdel-Aziz El-Bahi Street, Sousse 4000, Tunisia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Higher Institute of Management, University of Sousse, Abdel-Aziz El-Bahi Street, Sousse 4000, Tunisia","institution_ids":["https://openalex.org/I8636806"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046505962","display_name":"Hedi Kortas","orcid":null},"institutions":[{"id":"https://openalex.org/I8636806","display_name":"University of Sousse","ror":"https://ror.org/00dmpgj58","country_code":"TN","type":"education","lineage":["https://openalex.org/I8636806"]}],"countries":["TN"],"is_corresponding":false,"raw_author_name":"Hedi Kortas","raw_affiliation_strings":["Higher Institute of Management, University of Sousse, Abdel-Aziz El-Bahi Street, Sousse 4000, Tunisia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Higher Institute of Management, University of Sousse, Abdel-Aziz El-Bahi Street, Sousse 4000, Tunisia","institution_ids":["https://openalex.org/I8636806"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019696421","display_name":"Samir Benammou","orcid":null},"institutions":[{"id":"https://openalex.org/I166928557","display_name":"University of Monastir","ror":"https://ror.org/00nhtcg76","country_code":"TN","type":"education","lineage":["https://openalex.org/I166928557"]}],"countries":["TN"],"is_corresponding":false,"raw_author_name":"Samir Benammou","raw_affiliation_strings":["Faculty of Science, Computational Mathematics Laboratory, University of Monastir, Monastir 5000, Tunisia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Science, Computational Mathematics Laboratory, University of Monastir, Monastir 5000, Tunisia","institution_ids":["https://openalex.org/I166928557"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.11770189,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"24","issue":"04","first_page":"1450041","last_page":"1450041"},"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":0.9984999895095825,"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":0.9984999895095825,"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/T10282","display_name":"Financial Risk and Volatility Modeling","score":0.9976000189781189,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9950000047683716,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8292502760887146},{"id":"https://openalex.org/keywords/fractional-brownian-motion","display_name":"Fractional Brownian motion","score":0.772544264793396},{"id":"https://openalex.org/keywords/correlation-dimension","display_name":"Correlation dimension","score":0.695246696472168},{"id":"https://openalex.org/keywords/wavelet","display_name":"Wavelet","score":0.552087664604187},{"id":"https://openalex.org/keywords/gaussian-noise","display_name":"Gaussian noise","score":0.5477790236473083},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5303248763084412},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.456759512424469},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4435502886772156},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.4216436743736267},{"id":"https://openalex.org/keywords/gaussian-process","display_name":"Gaussian process","score":0.4143088459968567},{"id":"https://openalex.org/keywords/brownian-motion","display_name":"Brownian motion","score":0.39177632331848145},{"id":"https://openalex.org/keywords/fractal-dimension","display_name":"Fractal dimension","score":0.3878690004348755},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.385206401348114},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.38204553723335266},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.3750629425048828},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.19693449139595032},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1868806779384613},{"id":"https://openalex.org/keywords/fractal","display_name":"Fractal","score":0.1820453703403473},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.16965028643608093},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09671258926391602},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07579469680786133},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07302340865135193}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8292502760887146},{"id":"https://openalex.org/C108819105","wikidata":"https://www.wikidata.org/wiki/Q1143293","display_name":"Fractional Brownian motion","level":3,"score":0.772544264793396},{"id":"https://openalex.org/C110601934","wikidata":"https://www.wikidata.org/wiki/Q5172849","display_name":"Correlation dimension","level":4,"score":0.695246696472168},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.552087664604187},{"id":"https://openalex.org/C4199805","wikidata":"https://www.wikidata.org/wiki/Q2725903","display_name":"Gaussian noise","level":2,"score":0.5477790236473083},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5303248763084412},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.456759512424469},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4435502886772156},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.4216436743736267},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.4143088459968567},{"id":"https://openalex.org/C112401455","wikidata":"https://www.wikidata.org/wiki/Q178036","display_name":"Brownian motion","level":2,"score":0.39177632331848145},{"id":"https://openalex.org/C26546657","wikidata":"https://www.wikidata.org/wiki/Q1412452","display_name":"Fractal dimension","level":3,"score":0.3878690004348755},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.385206401348114},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.38204553723335266},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.3750629425048828},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.19693449139595032},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1868806779384613},{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.1820453703403473},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.16965028643608093},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09671258926391602},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07579469680786133},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07302340865135193},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127414500412","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127414500412","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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 Bifurcation and Chaos","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W94931019","https://openalex.org/W574370508","https://openalex.org/W1967071544","https://openalex.org/W1975426136","https://openalex.org/W1984391316","https://openalex.org/W2006079214","https://openalex.org/W2014402646","https://openalex.org/W2029401646","https://openalex.org/W2031753087","https://openalex.org/W2033288963","https://openalex.org/W2055084071","https://openalex.org/W2115755118","https://openalex.org/W2132984323","https://openalex.org/W2152328854","https://openalex.org/W2170793345","https://openalex.org/W4242546747","https://openalex.org/W4255272544"],"related_works":["https://openalex.org/W2373202200","https://openalex.org/W4390048237","https://openalex.org/W1573173092","https://openalex.org/W2753870633","https://openalex.org/W3021897514","https://openalex.org/W2165241701","https://openalex.org/W2375779197","https://openalex.org/W2774655044","https://openalex.org/W1989777550","https://openalex.org/W4256493607"],"abstract_inverted_index":{"In":[0],"this":[1,51],"paper,":[2],"we":[3,70,152],"study":[4],"the":[5,8,13,22,35,42,54,57,67,74,80,85,90,94,123,126,140,146,157,160,165,168,173,177],"behavior":[6],"of":[7,56,66,125,139,149,159,167],"correlation":[9,44,81,128,169],"dimension":[10,45,82,129,170],"estimated":[11,83,171],"using":[12,63],"Grassberger\u2013Procaccia":[14],"(GP)":[15],"algorithm":[16,175],"[Grassberger":[17],"&":[18],"Procaccia,":[19],"1983]":[20],"in":[21],"wavelet":[23,36,68],"domain":[24],"for":[25,73,135,145],"functions":[26],"belonging":[27],"to":[28,40,48,53,89,122],"H\u00f6lder":[29],"space.":[30],"We":[31],"prove":[32],"that,":[33,72],"as":[34,176],"scale":[37],"level":[38],"tends":[39,47],"infinity,":[41],"GP":[43,86,174],"estimate":[46],"zero.":[49,181],"Applying":[50],"result":[52,133],"trajectories":[55],"fractional":[58,75,95],"Brownian":[59],"motion":[60],"process":[61,78,101],"and":[62,114,164],"basic":[64],"properties":[65],"transform,":[69],"show":[71],"Gaussian":[76,96],"noise":[77,97,120],"(fGn),":[79],"by":[84,172],"procedure":[87],"converges":[88],"zero":[91],"value.":[92],"As":[93],"is":[98,179],"a":[99,136],"stochastic":[100],"with":[102],"1/f\u03b1":[103],"spectrum,":[104],"-1":[105],"<":[106,108],"\u03b1":[107],"1,":[109],"our":[110,132],"results":[111],"confirm":[112],"Osborne":[113],"Provenzale's":[115],"assertion":[116],"that":[117],"colored":[118],"random":[119,150],"leads":[121],"convergence":[124],"GP-based":[127],"estimator.":[130],"However,":[131],"holds":[134],"different":[137],"range":[138],"spectrum":[141],"exponent":[142,162],"values.":[143],"Moreover,":[144],"fGn":[147],"class":[148],"processes,":[151],"found":[153],"no":[154],"correspondence":[155],"between":[156],"value":[158,166],"scaling":[161],"H":[163],"latter":[178],"simply":[180]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}