{"id":"https://openalex.org/W2130259465","doi":"https://doi.org/10.1080/03610910802711743","title":"Exact Likelihood Equations for Autoregression Models with Multivariate Elliptically Contoured Distributions","display_name":"Exact Likelihood Equations for Autoregression Models with Multivariate Elliptically Contoured Distributions","publication_year":2009,"publication_date":"2009-02-24","ids":{"openalex":"https://openalex.org/W2130259465","doi":"https://doi.org/10.1080/03610910802711743","mag":"2130259465"},"language":"en","primary_location":{"id":"doi:10.1080/03610910802711743","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03610910802711743","pdf_url":null,"source":{"id":"https://openalex.org/S153329750","display_name":"Communications in Statistics - Simulation and Computation","issn_l":"0361-0918","issn":["0361-0918","1532-4141"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications in Statistics - Simulation and Computation","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/A5071642511","display_name":"B. Tarami","orcid":"https://orcid.org/0000-0002-2222-8853"},"institutions":[{"id":"https://openalex.org/I3121641575","display_name":"Yasouj University","ror":"https://ror.org/05sy5hm57","country_code":"IR","type":"education","lineage":["https://openalex.org/I3121641575"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"B. Tarami","raw_affiliation_strings":["Department of Mathematics, College of Sciences , Yasouj University , Yasouj , Iran","Department of Mathematics, College of Sciences; Yasouj University; Yasouj Iran"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Sciences , Yasouj University , Yasouj , Iran","institution_ids":["https://openalex.org/I3121641575"]},{"raw_affiliation_string":"Department of Mathematics, College of Sciences; Yasouj University; Yasouj Iran","institution_ids":["https://openalex.org/I3121641575"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087108662","display_name":"Zahra Khodadadi","orcid":"https://orcid.org/0000-0001-8242-762X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Z. Khodadadi","raw_affiliation_strings":["Department of Statistics , Islamic Azad University, Science & Research Branch , Tehran , Iran","Department of statistics, Islamic Azad University, Science and Research Branch, Tehran, Iran"],"affiliations":[{"raw_affiliation_string":"Department of Statistics , Islamic Azad University, Science & Research Branch , Tehran , Iran","institution_ids":[]},{"raw_affiliation_string":"Department of statistics, Islamic Azad University, Science and Research Branch, Tehran, Iran","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5071642511"],"corresponding_institution_ids":["https://openalex.org/I3121641575"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.22195506,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"38","issue":"5","first_page":"976","last_page":"989"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10282","display_name":"Financial Risk and Volatility Modeling","score":0.9983999729156494,"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":0.9983999729156494,"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/T11186","display_name":"Hydrology and Drought Analysis","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/2306","display_name":"Global and Planetary Change"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.9797999858856201,"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/autoregressive-model","display_name":"Autoregressive model","score":0.8365784287452698},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.8106953501701355},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.6355105638504028},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5833289623260498},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5809235572814941},{"id":"https://openalex.org/keywords/cauchy-distribution","display_name":"Cauchy distribution","score":0.5774474143981934},{"id":"https://openalex.org/keywords/likelihood-function","display_name":"Likelihood function","score":0.530043363571167},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.47545525431632996},{"id":"https://openalex.org/keywords/multivariate-normal-distribution","display_name":"Multivariate normal distribution","score":0.4428616762161255},{"id":"https://openalex.org/keywords/estimating-equations","display_name":"Estimating equations","score":0.4333621859550476},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.42399245500564575},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.40872496366500854},{"id":"https://openalex.org/keywords/estimation-theory","display_name":"Estimation theory","score":0.40702471137046814},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23229876160621643},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.06868043541908264}],"concepts":[{"id":"https://openalex.org/C159877910","wikidata":"https://www.wikidata.org/wiki/Q2202883","display_name":"Autoregressive model","level":2,"score":0.8365784287452698},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.8106953501701355},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6355105638504028},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5833289623260498},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5809235572814941},{"id":"https://openalex.org/C49344536","wikidata":"https://www.wikidata.org/wiki/Q726441","display_name":"Cauchy distribution","level":2,"score":0.5774474143981934},{"id":"https://openalex.org/C89106044","wikidata":"https://www.wikidata.org/wiki/Q45284","display_name":"Likelihood function","level":3,"score":0.530043363571167},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.47545525431632996},{"id":"https://openalex.org/C177384507","wikidata":"https://www.wikidata.org/wiki/Q1149000","display_name":"Multivariate normal distribution","level":3,"score":0.4428616762161255},{"id":"https://openalex.org/C204016326","wikidata":"https://www.wikidata.org/wiki/Q5401384","display_name":"Estimating equations","level":3,"score":0.4333621859550476},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.42399245500564575},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.40872496366500854},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.40702471137046814},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23229876160621643},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.06868043541908264},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/03610910802711743","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03610910802711743","pdf_url":null,"source":{"id":"https://openalex.org/S153329750","display_name":"Communications in Statistics - Simulation and Computation","issn_l":"0361-0918","issn":["0361-0918","1532-4141"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications in Statistics - Simulation and Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.41999998688697815}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W2033280533","https://openalex.org/W2035202495","https://openalex.org/W2063146705","https://openalex.org/W2122861691","https://openalex.org/W3122658526","https://openalex.org/W4292963524","https://openalex.org/W4300246981"],"related_works":["https://openalex.org/W2083133624","https://openalex.org/W4290005101","https://openalex.org/W2120595071","https://openalex.org/W3191227317","https://openalex.org/W2499041866","https://openalex.org/W3167036484","https://openalex.org/W2254601135","https://openalex.org/W1598553450","https://openalex.org/W2094510543","https://openalex.org/W2035202495"],"abstract_inverted_index":{"Abstract":[0],"The":[1,59],"multivariate":[2,17,29],"elliptically":[3,30],"contoured":[4,31],"distributions":[5,24],"provide":[6],"a":[7],"viable":[8],"framework":[9],"for":[10,40],"modeling":[11],"time-series":[12],"data.":[13,58,76],"It":[14],"includes":[15],"the":[16,36,41,49,57,74],"normal,":[18],"power":[19],"exponential,":[20],"t,":[21],"and":[22,52,71],"Cauchy":[23],"as":[25],"special":[26],"cases.":[27],"For":[28],"autoregressive":[32],"models,":[33],"we":[34],"derive":[35],"exact":[37],"likelihood":[38,61],"equations":[39,51],"model":[42],"parameters.":[43],"They":[44],"are":[45,63],"closely":[46],"related":[47],"to":[48],"Yule-Walker":[50],"involve":[53],"simple":[54],"function":[55],"of":[56],"maximum":[60],"estimators":[62],"obtained":[64],"by":[65],"alternately":[66],"solving":[67],"two":[68],"linear":[69],"systems":[70],"illustrated":[72],"using":[73],"simulation":[75]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}