{"id":"https://openalex.org/W1976157318","doi":"https://doi.org/10.1137/090768680","title":"New Method of Order Estimation for ARMA/ARMAX Processes","display_name":"New Method of Order Estimation for ARMA/ARMAX Processes","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W1976157318","doi":"https://doi.org/10.1137/090768680","mag":"1976157318"},"language":"en","primary_location":{"id":"doi:10.1137/090768680","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090768680","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","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/A5112593034","display_name":"Han-Fu Chen","orcid":"https://orcid.org/0000-0003-3429-3270"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Han-Fu Chen","raw_affiliation_strings":["hfchen@iss.ac.cn#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"hfchen@iss.ac.cn#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101465051","display_name":"Wenxiao Zhao","orcid":"https://orcid.org/0000-0002-0371-5664"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wen-Xiao Zhao","raw_affiliation_strings":["wxzhao@mail.tsinghua.edu.cn#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"wxzhao@mail.tsinghua.edu.cn#TAB#","institution_ids":["https://openalex.org/I99065089"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.536,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.8552482,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"48","issue":"6","first_page":"4157","last_page":"4176"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11443","display_name":"Advanced Statistical Process Monitoring","score":0.9939000010490417,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11443","display_name":"Advanced Statistical Process Monitoring","score":0.9939000010490417,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11447","display_name":"Blind Source Separation Techniques","score":0.9929999709129333,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.9926999807357788,"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/mathematics","display_name":"Mathematics","score":0.852893590927124},{"id":"https://openalex.org/keywords/independent-and-identically-distributed-random-variables","display_name":"Independent and identically distributed random variables","score":0.7480713129043579},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5942755937576294},{"id":"https://openalex.org/keywords/covariance-matrix","display_name":"Covariance matrix","score":0.5202411413192749},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4810812175273895},{"id":"https://openalex.org/keywords/autoregressive\u2013moving-average-model","display_name":"Autoregressive\u2013moving-average model","score":0.4762432873249054},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.47368600964546204},{"id":"https://openalex.org/keywords/infinity","display_name":"Infinity","score":0.4339510202407837},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.43291938304901123},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4240944981575012},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3760543465614319},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.34908556938171387},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.34491994976997375},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3213387429714203},{"id":"https://openalex.org/keywords/autoregressive-model","display_name":"Autoregressive model","score":0.19212055206298828},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17989182472229004}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.852893590927124},{"id":"https://openalex.org/C141513077","wikidata":"https://www.wikidata.org/wiki/Q378542","display_name":"Independent and identically distributed random variables","level":3,"score":0.7480713129043579},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5942755937576294},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.5202411413192749},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4810812175273895},{"id":"https://openalex.org/C74883015","wikidata":"https://www.wikidata.org/wiki/Q290467","display_name":"Autoregressive\u2013moving-average model","level":3,"score":0.4762432873249054},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.47368600964546204},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.4339510202407837},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.43291938304901123},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4240944981575012},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3760543465614319},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.34908556938171387},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.34491994976997375},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3213387429714203},{"id":"https://openalex.org/C159877910","wikidata":"https://www.wikidata.org/wiki/Q2202883","display_name":"Autoregressive model","level":2,"score":0.19212055206298828},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17989182472229004},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/090768680","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090768680","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1501203061","https://openalex.org/W1505725179","https://openalex.org/W1509685104","https://openalex.org/W1569320505","https://openalex.org/W1967216868","https://openalex.org/W1987504715","https://openalex.org/W2040868087","https://openalex.org/W2041001113","https://openalex.org/W2054658115","https://openalex.org/W2068835296","https://openalex.org/W2075269708","https://openalex.org/W2099280778","https://openalex.org/W2114160172","https://openalex.org/W2122518971","https://openalex.org/W2126509795","https://openalex.org/W2137894152","https://openalex.org/W2142635246","https://openalex.org/W2143082178","https://openalex.org/W2150642605","https://openalex.org/W2170629618","https://openalex.org/W2172027528","https://openalex.org/W2313953460","https://openalex.org/W2330166836","https://openalex.org/W2798461040","https://openalex.org/W2895512211","https://openalex.org/W3149745985"],"related_works":["https://openalex.org/W2347733609","https://openalex.org/W2066502241","https://openalex.org/W2605475288","https://openalex.org/W2292976891","https://openalex.org/W4240383795","https://openalex.org/W4245457074","https://openalex.org/W2128683635","https://openalex.org/W2008809748","https://openalex.org/W2140857733","https://openalex.org/W2951620698"],"abstract_inverted_index":{"Let":[0],"the":[1,7,46,56,59,71,76,87,101,109,116],"observation":[2],"$\\{y_k\\}$":[3],"be":[4],"generated":[5],"by":[6],"multivariate":[8],"ARMA":[9],"process":[10],"$A(z)y_k=C(z)w_k$":[11],"with":[12,33,86,119],"unknown":[13,37],"coefficients":[14],"$\\theta_A$,":[15],"$\\theta_C$":[16],"and":[17,27,36,70],"orders":[18,47,102,118],"$(p,r)$,":[19],"where":[20],"$\\{w_k\\}$":[21],"is":[22,49,62,96],"a":[23,67],"sequence":[24],"of":[25,55,103],"independent":[26],"identically":[28],"distributed":[29],"(i.i.d.)":[30],"random":[31],"vectors":[32],"zero":[34],"mean":[35],"covariance":[38],"matrix":[39],"$R_w>0$.":[40],"A":[41],"new":[42,60,91],"method":[43,61,95],"for":[44],"estimating":[45],"$(p,r)$":[48],"introduced.":[50],"In":[51],"contrast":[52],"to":[53,81,99,113,115,125],"most":[54],"existing":[57],"results,":[58],"not":[63],"based":[64],"on":[65],"optimizing":[66],"certain":[68],"criterion,":[69],"order":[72],"estimates":[73,110],"given":[74],"in":[75,84],"paper":[77],"are":[78,111],"rather":[79],"easy":[80],"update":[82],"computationally":[83],"comparison":[85],"criterion-optimization\u2013based":[88],"methods":[89],"when":[90],"data":[92],"arrive.":[93],"The":[94],"then":[97],"extended":[98],"determining":[100],"ARMAX":[104],"processes.":[105],"Under":[106],"reasonable":[107],"conditions":[108],"proved":[112],"converge":[114],"true":[117],"probability":[120],"one":[121],"as":[122],"time":[123],"tends":[124],"infinity.":[126]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":5}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}