{"id":"https://openalex.org/W4205111948","doi":"https://doi.org/10.3390/sym14010158","title":"High-Dimensional Conditional Covariance Matrices Estimation Using a Factor-GARCH Model","display_name":"High-Dimensional Conditional Covariance Matrices Estimation Using a Factor-GARCH Model","publication_year":2022,"publication_date":"2022-01-13","ids":{"openalex":"https://openalex.org/W4205111948","doi":"https://doi.org/10.3390/sym14010158"},"language":"en","primary_location":{"id":"doi:10.3390/sym14010158","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14010158","pdf_url":"https://www.mdpi.com/2073-8994/14/1/158/pdf?version=1642145803","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/14/1/158/pdf?version=1642145803","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100369478","display_name":"Xiaoling Li","orcid":"https://orcid.org/0000-0001-5920-7784"},"institutions":[{"id":"https://openalex.org/I37987034","display_name":"Guangzhou University","ror":"https://ror.org/05ar8rn06","country_code":"CN","type":"education","lineage":["https://openalex.org/I37987034"]},{"id":"https://openalex.org/I101479585","display_name":"South China Agricultural University","ror":"https://ror.org/05v9jqt67","country_code":"CN","type":"education","lineage":["https://openalex.org/I101479585"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaoling Li","raw_affiliation_strings":["College of Mathematics and Informatics, South China Agricultural University, Guangzhou 510642, China","School of Economics and Statistics, Guangzhou University, Guangzhou 510006, China"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Informatics, South China Agricultural University, Guangzhou 510642, China","institution_ids":["https://openalex.org/I101479585"]},{"raw_affiliation_string":"School of Economics and Statistics, Guangzhou University, Guangzhou 510006, China","institution_ids":["https://openalex.org/I37987034"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080579882","display_name":"Xingfa Zhang","orcid":"https://orcid.org/0000-0002-5816-7730"},"institutions":[{"id":"https://openalex.org/I37987034","display_name":"Guangzhou University","ror":"https://ror.org/05ar8rn06","country_code":"CN","type":"education","lineage":["https://openalex.org/I37987034"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xingfa Zhang","raw_affiliation_strings":["School of Economics and Statistics, Guangzhou University, Guangzhou 510006, China"],"affiliations":[{"raw_affiliation_string":"School of Economics and Statistics, Guangzhou University, Guangzhou 510006, China","institution_ids":["https://openalex.org/I37987034"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039755457","display_name":"Yuan Li","orcid":"https://orcid.org/0000-0001-9158-6390"},"institutions":[{"id":"https://openalex.org/I37987034","display_name":"Guangzhou University","ror":"https://ror.org/05ar8rn06","country_code":"CN","type":"education","lineage":["https://openalex.org/I37987034"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuan Li","raw_affiliation_strings":["School of Economics and Statistics, Guangzhou University, Guangzhou 510006, China"],"affiliations":[{"raw_affiliation_string":"School of Economics and Statistics, Guangzhou University, Guangzhou 510006, China","institution_ids":["https://openalex.org/I37987034"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5080579882"],"corresponding_institution_ids":["https://openalex.org/I37987034"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.0398,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.76230848,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"14","issue":"1","first_page":"158","last_page":"158"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10282","display_name":"Financial Risk and Volatility Modeling","score":0.9994999766349792,"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":0.9994999766349792,"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":0.9919999837875366,"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/T10136","display_name":"Statistical Methods and Inference","score":0.9785000085830688,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/conditional-variance","display_name":"Conditional variance","score":0.7783409357070923},{"id":"https://openalex.org/keywords/estimation-of-covariance-matrices","display_name":"Estimation of covariance matrices","score":0.6859962940216064},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.6678205728530884},{"id":"https://openalex.org/keywords/covariance-matrix","display_name":"Covariance matrix","score":0.6586529612541199},{"id":"https://openalex.org/keywords/autoregressive-conditional-heteroskedasticity","display_name":"Autoregressive conditional heteroskedasticity","score":0.6398841738700867},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.6226576566696167},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5455976128578186},{"id":"https://openalex.org/keywords/law-of-total-covariance","display_name":"Law of total covariance","score":0.49215763807296753},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.48876023292541504},{"id":"https://openalex.org/keywords/mat\u00e9rn-covariance-function","display_name":"Mat\u00e9rn covariance function","score":0.4377387762069702},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.3798080384731293},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3318501114845276},{"id":"https://openalex.org/keywords/covariance-intersection","display_name":"Covariance intersection","score":0.30519580841064453},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2933550775051117}],"concepts":[{"id":"https://openalex.org/C21430997","wikidata":"https://www.wikidata.org/wiki/Q5159279","display_name":"Conditional variance","level":4,"score":0.7783409357070923},{"id":"https://openalex.org/C180877172","wikidata":"https://www.wikidata.org/wiki/Q5401390","display_name":"Estimation of covariance matrices","level":3,"score":0.6859962940216064},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.6678205728530884},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.6586529612541199},{"id":"https://openalex.org/C23922673","wikidata":"https://www.wikidata.org/wiki/Q180752","display_name":"Autoregressive conditional heteroskedasticity","level":3,"score":0.6398841738700867},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.6226576566696167},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5455976128578186},{"id":"https://openalex.org/C126372606","wikidata":"https://www.wikidata.org/wiki/Q6503511","display_name":"Law of total covariance","level":5,"score":0.49215763807296753},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48876023292541504},{"id":"https://openalex.org/C118006245","wikidata":"https://www.wikidata.org/wiki/Q6792079","display_name":"Mat\u00e9rn covariance function","level":5,"score":0.4377387762069702},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.3798080384731293},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3318501114845276},{"id":"https://openalex.org/C83042196","wikidata":"https://www.wikidata.org/wiki/Q5178898","display_name":"Covariance intersection","level":4,"score":0.30519580841064453},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2933550775051117},{"id":"https://openalex.org/C91602232","wikidata":"https://www.wikidata.org/wiki/Q756115","display_name":"Volatility (finance)","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym14010158","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14010158","pdf_url":"https://www.mdpi.com/2073-8994/14/1/158/pdf?version=1642145803","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:a71ddc946fca43a295d13dcb4b720be5","is_oa":true,"landing_page_url":"https://doaj.org/article/a71ddc946fca43a295d13dcb4b720be5","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 14, Iss 1, p 158 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/1/158/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14010158","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":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym14010158","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14010158","pdf_url":"https://www.mdpi.com/2073-8994/14/1/158/pdf?version=1642145803","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.44999998807907104,"id":"https://metadata.un.org/sdg/8","display_name":"Decent work and economic growth"}],"awards":[{"id":"https://openalex.org/G523974011","display_name":null,"funder_award_id":"11731015","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5938486007","display_name":null,"funder_award_id":"11701116","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":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4205111948.pdf","grobid_xml":"https://content.openalex.org/works/W4205111948.grobid-xml"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W105317347","https://openalex.org/W939881955","https://openalex.org/W1538635905","https://openalex.org/W1727659491","https://openalex.org/W1977480757","https://openalex.org/W1998968611","https://openalex.org/W2006875428","https://openalex.org/W2026102811","https://openalex.org/W2028726096","https://openalex.org/W2038395331","https://openalex.org/W2040373108","https://openalex.org/W2063593194","https://openalex.org/W2073681337","https://openalex.org/W2083771855","https://openalex.org/W2091536878","https://openalex.org/W2125791736","https://openalex.org/W2135086139","https://openalex.org/W2149498682","https://openalex.org/W2166215547","https://openalex.org/W2170813608","https://openalex.org/W2193043149","https://openalex.org/W2921720134","https://openalex.org/W2950126918","https://openalex.org/W3040514440","https://openalex.org/W3098826229","https://openalex.org/W3101440325","https://openalex.org/W3114379428","https://openalex.org/W3122029670","https://openalex.org/W3125564657","https://openalex.org/W4235146513","https://openalex.org/W4254913624","https://openalex.org/W6632348997","https://openalex.org/W6634927326","https://openalex.org/W6684669166","https://openalex.org/W6684930130","https://openalex.org/W6807091881"],"related_works":["https://openalex.org/W69681753","https://openalex.org/W4386993326","https://openalex.org/W2022823194","https://openalex.org/W2109377650","https://openalex.org/W2126916073","https://openalex.org/W3211883524","https://openalex.org/W341081156","https://openalex.org/W2050026105","https://openalex.org/W2169046449","https://openalex.org/W3138022501"],"abstract_inverted_index":{"Estimation":[0],"of":[1,32,37,53,66,102],"a":[2,47,54,58,67],"conditional":[3,69,103],"covariance":[4,23,70,104],"matrix":[5],"is":[6,25,96,126],"an":[7],"interesting":[8],"and":[9,15,57,77,92,114],"important":[10],"research":[11],"topic":[12],"in":[13,89],"statistics":[14],"econometrics.":[16],"However,":[17],"modelling":[18],"ultra-high":[19],"dimensional":[20],"dynamic":[21],"(conditional)":[22],"structures":[24],"known":[26],"to":[27,62,85,98,119,128],"suffer":[28],"from":[29],"the":[30,35,51,64,87,90,93,100,111,130],"curse":[31],"dimensionality":[33],"or":[34],"problem":[36],"singularity.":[38],"To":[39],"partially":[40],"solve":[41],"this":[42,44],"problem,":[43],"paper":[45],"establishes":[46],"model":[48,56,61],"by":[49],"combining":[50],"ideas":[52],"factor":[55],"symmetric":[59],"GARCH":[60],"describe":[63],"dynamics":[65],"high-dimensional":[68],"matrix.":[71,105],"Quasi":[72],"maximum":[73],"likelihood":[74],"estimation":[75,80,101],"(QMLE)":[76],"least":[78],"square":[79],"(LSE)":[81],"methods":[82],"are":[83,108,117],"used":[84],"estimate":[86],"parameters":[88],"model,":[91],"plug-in":[94],"method":[95],"introduced":[97],"obtain":[99],"Asymptotic":[106],"properties":[107],"established":[109],"for":[110],"proposed":[112],"method,":[113],"simulation":[115],"studies":[116],"given":[118],"demonstrate":[120],"its":[121],"performance.":[122],"A":[123],"financial":[124],"application":[125],"presented":[127],"support":[129],"methodology.":[131]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}