{"id":"https://openalex.org/W7135179401","doi":"https://doi.org/10.3390/e28030326","title":"Quasi-Maximum Exponential Likelihood Estimation of Conditional Quantiles for GARCH Models Based on High-Frequency Augmented Data","display_name":"Quasi-Maximum Exponential Likelihood Estimation of Conditional Quantiles for GARCH Models Based on High-Frequency Augmented Data","publication_year":2026,"publication_date":"2026-03-13","ids":{"openalex":"https://openalex.org/W7135179401","doi":"https://doi.org/10.3390/e28030326","pmid":"https://pubmed.ncbi.nlm.nih.gov/41899978"},"language":"en","primary_location":{"id":"doi:10.3390/e28030326","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e28030326","pdf_url":null,"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://doi.org/10.3390/e28030326","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5129046562","display_name":"Zhenming Zhang","orcid":null},"institutions":[{"id":"https://openalex.org/I194450716","display_name":"Jilin University","ror":"https://ror.org/00js3aw79","country_code":"CN","type":"education","lineage":["https://openalex.org/I194450716"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhenming Zhang","raw_affiliation_strings":["School of Mathematics, Jilin University, Changchun 130012, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Jilin University, Changchun 130012, China","institution_ids":["https://openalex.org/I194450716"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021977142","display_name":"Shishun Zhao","orcid":null},"institutions":[{"id":"https://openalex.org/I194450716","display_name":"Jilin University","ror":"https://ror.org/00js3aw79","country_code":"CN","type":"education","lineage":["https://openalex.org/I194450716"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shishun Zhao","raw_affiliation_strings":["School of Mathematics, Jilin University, Changchun 130012, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Jilin University, Changchun 130012, China","institution_ids":["https://openalex.org/I194450716"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5128942752","display_name":"Jianhua Cheng","orcid":null},"institutions":[{"id":"https://openalex.org/I194450716","display_name":"Jilin University","ror":"https://ror.org/00js3aw79","country_code":"CN","type":"education","lineage":["https://openalex.org/I194450716"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jianhua Cheng","raw_affiliation_strings":["School of Mathematics, Jilin University, Changchun 130012, China"],"raw_orcid":"https://orcid.org/0000-0002-8615-1496","affiliations":[{"raw_affiliation_string":"School of Mathematics, Jilin University, Changchun 130012, China","institution_ids":["https://openalex.org/I194450716"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5129039616","display_name":"Anze Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I194450716","display_name":"Jilin University","ror":"https://ror.org/00js3aw79","country_code":"CN","type":"education","lineage":["https://openalex.org/I194450716"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Anze Wang","raw_affiliation_strings":["School of Mathematics, Jilin University, Changchun 130012, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Jilin University, Changchun 130012, China","institution_ids":["https://openalex.org/I194450716"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I194450716"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.27277448,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"28","issue":"3","first_page":"326","last_page":"326"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10282","display_name":"Financial Risk and Volatility Modeling","score":0.9886000156402588,"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":0.9886000156402588,"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/T10067","display_name":"Stochastic processes and financial applications","score":0.00139999995008111,"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/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.0008999999845400453,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.7656000256538391},{"id":"https://openalex.org/keywords/autoregressive-conditional-heteroskedasticity","display_name":"Autoregressive conditional heteroskedasticity","score":0.7053999900817871},{"id":"https://openalex.org/keywords/quantile","display_name":"Quantile","score":0.656499981880188},{"id":"https://openalex.org/keywords/volatility","display_name":"Volatility (finance)","score":0.579800009727478},{"id":"https://openalex.org/keywords/statistic","display_name":"Statistic","score":0.5393999814987183},{"id":"https://openalex.org/keywords/test-statistic","display_name":"Test statistic","score":0.37770000100135803},{"id":"https://openalex.org/keywords/asymptotic-distribution","display_name":"Asymptotic distribution","score":0.37459999322891235},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.36629998683929443},{"id":"https://openalex.org/keywords/stochastic-volatility","display_name":"Stochastic volatility","score":0.3650999963283539}],"concepts":[{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.7656000256538391},{"id":"https://openalex.org/C23922673","wikidata":"https://www.wikidata.org/wiki/Q180752","display_name":"Autoregressive conditional heteroskedasticity","level":3,"score":0.7053999900817871},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.6952999830245972},{"id":"https://openalex.org/C118671147","wikidata":"https://www.wikidata.org/wiki/Q578714","display_name":"Quantile","level":2,"score":0.656499981880188},{"id":"https://openalex.org/C91602232","wikidata":"https://www.wikidata.org/wiki/Q756115","display_name":"Volatility (finance)","level":2,"score":0.579800009727478},{"id":"https://openalex.org/C89128539","wikidata":"https://www.wikidata.org/wiki/Q1949963","display_name":"Statistic","level":2,"score":0.5393999814987183},{"id":"https://openalex.org/C169857963","wikidata":"https://www.wikidata.org/wiki/Q1461038","display_name":"Test statistic","level":3,"score":0.37770000100135803},{"id":"https://openalex.org/C65778772","wikidata":"https://www.wikidata.org/wiki/Q12345341","display_name":"Asymptotic distribution","level":3,"score":0.37459999322891235},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3675999939441681},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.36629998683929443},{"id":"https://openalex.org/C85393063","wikidata":"https://www.wikidata.org/wiki/Q596307","display_name":"Stochastic volatility","level":3,"score":0.3650999963283539},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36250001192092896},{"id":"https://openalex.org/C96250715","wikidata":"https://www.wikidata.org/wiki/Q965330","display_name":"Estimation","level":2,"score":0.35350000858306885},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3531000018119812},{"id":"https://openalex.org/C26359558","wikidata":"https://www.wikidata.org/wiki/Q7269462","display_name":"Quasi-maximum likelihood","level":4,"score":0.3416999876499176},{"id":"https://openalex.org/C43555835","wikidata":"https://www.wikidata.org/wiki/Q2300258","display_name":"Conditional probability distribution","level":2,"score":0.3393000066280365},{"id":"https://openalex.org/C21430997","wikidata":"https://www.wikidata.org/wiki/Q5159279","display_name":"Conditional variance","level":4,"score":0.3345000147819519},{"id":"https://openalex.org/C204036174","wikidata":"https://www.wikidata.org/wiki/Q909380","display_name":"Stock (firearms)","level":2,"score":0.3296999931335449},{"id":"https://openalex.org/C2780299701","wikidata":"https://www.wikidata.org/wiki/Q475000","display_name":"Stock market","level":3,"score":0.3163999915122986},{"id":"https://openalex.org/C19244329","wikidata":"https://www.wikidata.org/wiki/Q208697","display_name":"Financial market","level":2,"score":0.3093999922275543},{"id":"https://openalex.org/C199163554","wikidata":"https://www.wikidata.org/wiki/Q1681619","display_name":"Univariate","level":3,"score":0.30550000071525574},{"id":"https://openalex.org/C2781117939","wikidata":"https://www.wikidata.org/wiki/Q5374245","display_name":"Empirical likelihood","level":3,"score":0.29649999737739563},{"id":"https://openalex.org/C2778705799","wikidata":"https://www.wikidata.org/wiki/Q2823610","display_name":"Financial asset","level":2,"score":0.2687000036239624},{"id":"https://openalex.org/C63817138","wikidata":"https://www.wikidata.org/wiki/Q3455889","display_name":"Quantile regression","level":2,"score":0.2639000117778778},{"id":"https://openalex.org/C9483764","wikidata":"https://www.wikidata.org/wiki/Q585740","display_name":"Likelihood-ratio test","level":2,"score":0.25369998812675476},{"id":"https://openalex.org/C89106044","wikidata":"https://www.wikidata.org/wiki/Q45284","display_name":"Likelihood function","level":3,"score":0.25099998712539673}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/e28030326","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e28030326","pdf_url":null,"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:41899978","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/41899978","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:pubmedcentral.nih.gov:13025681","is_oa":true,"landing_page_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC13025681/","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC13025681/pdf/entropy-28-00326.pdf","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:acf255a039924e1795c1b15c562f5d6f","is_oa":true,"landing_page_url":"https://doaj.org/article/acf255a039924e1795c1b15c562f5d6f","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 28, Iss 3, p 326 (2026)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/e28030326","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e28030326","pdf_url":null,"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/G1164530782","display_name":null,"funder_award_id":"12071176","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G408818585","display_name":null,"funder_award_id":"12271231","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1578815837","https://openalex.org/W1984570338","https://openalex.org/W1991620995","https://openalex.org/W1991968032","https://openalex.org/W1994411832","https://openalex.org/W1999996900","https://openalex.org/W2002466177","https://openalex.org/W2003941523","https://openalex.org/W2012780930","https://openalex.org/W2021869006","https://openalex.org/W2026065939","https://openalex.org/W2030339186","https://openalex.org/W2075721156","https://openalex.org/W2079647269","https://openalex.org/W2146399390","https://openalex.org/W2165429427","https://openalex.org/W2540698443","https://openalex.org/W2743696592","https://openalex.org/W3094874664","https://openalex.org/W3095114851","https://openalex.org/W4241653265","https://openalex.org/W4400594079","https://openalex.org/W4409844937"],"related_works":[],"abstract_inverted_index":{"GARCH":[0,67,121,176],"models":[1,89,177],"play":[2],"a":[3],"fundamental":[4],"role":[5],"in":[6,10,105,185],"modeling":[7],"time-varying":[8],"volatility":[9,76,95],"financial":[11,16],"return":[12],"series.":[13],"In":[14],"practice,":[15],"returns":[17],"are":[18,90,102,154],"also":[19],"well":[20],"known":[21],"to":[22,61,92,168,182],"exhibit":[23],"heavy-tailed":[24],"distributions,":[25],"which":[26,69],"naturally":[27],"motivates":[28],"the":[29,49,52,62,148],"use":[30],"of":[31,55,64,147],"quasi-maximum":[32],"exponential":[33],"likelihood":[34],"estimation":[35,117,188],"(QMELE)":[36],"for":[37,118,127,140],"accurately":[38],"capturing":[39],"tail":[40],"behavior":[41],"and":[42,97,131,134,151,156],"risk":[43],"measures":[44],"such":[45],"as":[46],"Value-at-Risk.":[47],"At":[48],"same":[50],"time,":[51],"increasing":[53],"availability":[54],"intraday":[56,71,94],"high-frequency":[57,65,119,179],"data":[58,81],"has":[59],"led":[60],"development":[63],"augmented":[66,120],"models,":[68],"incorporate":[70],"information":[72,180],"into":[73],"conventional":[74],"low-frequency":[75,107,192],"frameworks.":[77],"By":[78],"exploiting":[79],"transaction-level":[80],"recorded":[82],"at":[83],"very":[84],"fine":[85],"time":[86],"scales,":[87],"these":[88],"able":[91],"capture":[93],"dynamics":[96],"market":[98],"microstructure":[99],"effects":[100],"that":[101,174],"not":[103],"reflected":[104],"standard":[106],"observations.":[108],"Against":[109],"this":[110,112],"background,":[111],"paper":[113],"studies":[114],"conditional":[115,132,186],"quantile":[116,187],"models.":[122],"We":[123],"develop":[124],"QMELE-based":[125],"estimators":[126,150],"both":[128],"model":[129,142],"parameters":[130],"quantiles,":[133],"construct":[135],"an":[136],"adjusted":[137],"test":[138,152],"statistic":[139,153],"assessing":[141],"adequacy.":[143],"The":[144],"asymptotic":[145],"properties":[146],"proposed":[149],"established,":[155],"their":[157],"finite-sample":[158],"performance":[159],"is":[160],"examined":[161],"through":[162],"extensive":[163],"simulation":[164],"studies.":[165],"Empirical":[166],"applications":[167],"three":[169],"major":[170],"stock":[171],"indices":[172],"demonstrate":[173],"augmenting":[175],"with":[178,190],"leads":[181],"substantial":[183],"improvements":[184],"compared":[189],"traditional":[191],"approaches.":[193]},"counts_by_year":[],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2026-03-14T00:00:00"}