{"id":"https://openalex.org/W1985914742","doi":"https://doi.org/10.1109/ciss.2012.6310847","title":"On the convergence of the spectral density of autoregressive approximations via empirical covariance estimates","display_name":"On the convergence of the spectral density of autoregressive approximations via empirical covariance estimates","publication_year":2012,"publication_date":"2012-03-01","ids":{"openalex":"https://openalex.org/W1985914742","doi":"https://doi.org/10.1109/ciss.2012.6310847","mag":"1985914742"},"language":"en","primary_location":{"id":"doi:10.1109/ciss.2012.6310847","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ciss.2012.6310847","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 46th Annual Conference on Information Sciences and Systems (CISS)","raw_type":"proceedings-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/A5043029595","display_name":"Syamantak Datta Gupta","orcid":null},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Syamantak Datta Gupta","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON, Canada","Department of Electrical and computer Engineering, University of Waterloo, ON, N2L 3G1, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON, Canada","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"Department of Electrical and computer Engineering, University of Waterloo, ON, N2L 3G1, Canada","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061577384","display_name":"Ravi R. Mazumdar","orcid":"https://orcid.org/0000-0002-0968-0925"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Ravi R. Mazumdar","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON, Canada","Department of Electrical and computer Engineering, University of Waterloo, ON, N2L 3G1, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON, Canada","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"Department of Electrical and computer Engineering, University of Waterloo, ON, N2L 3G1, Canada","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5043029595"],"corresponding_institution_ids":["https://openalex.org/I151746483"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.07998917,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"137","issue":null,"first_page":"1","last_page":"6"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.9973000288009644,"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"}},"topics":[{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.9973000288009644,"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"}},{"id":"https://openalex.org/T10282","display_name":"Financial Risk and Volatility Modeling","score":0.9944000244140625,"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/T11236","display_name":"Control Systems and Identification","score":0.9933000206947327,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/autoregressive-model","display_name":"Autoregressive model","score":0.86665940284729},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.706999659538269},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6163173913955688},{"id":"https://openalex.org/keywords/star-model","display_name":"STAR model","score":0.5874372720718384},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5587859749794006},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5039255023002625},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.43024155497550964},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.42991313338279724},{"id":"https://openalex.org/keywords/autoregressive-integrated-moving-average","display_name":"Autoregressive integrated moving average","score":0.34322088956832886},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.31251323223114014},{"id":"https://openalex.org/keywords/time-series","display_name":"Time series","score":0.20968374609947205}],"concepts":[{"id":"https://openalex.org/C159877910","wikidata":"https://www.wikidata.org/wiki/Q2202883","display_name":"Autoregressive model","level":2,"score":0.86665940284729},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.706999659538269},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6163173913955688},{"id":"https://openalex.org/C194657046","wikidata":"https://www.wikidata.org/wiki/Q7394685","display_name":"STAR model","level":4,"score":0.5874372720718384},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5587859749794006},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5039255023002625},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.43024155497550964},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.42991313338279724},{"id":"https://openalex.org/C24338571","wikidata":"https://www.wikidata.org/wiki/Q2566298","display_name":"Autoregressive integrated moving average","level":3,"score":0.34322088956832886},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.31251323223114014},{"id":"https://openalex.org/C151406439","wikidata":"https://www.wikidata.org/wiki/Q186588","display_name":"Time series","level":2,"score":0.20968374609947205},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/ciss.2012.6310847","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ciss.2012.6310847","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 46th Annual Conference on Information Sciences and Systems (CISS)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W274693873","https://openalex.org/W566302253","https://openalex.org/W633754876","https://openalex.org/W1634521568","https://openalex.org/W1965478760","https://openalex.org/W1979847668","https://openalex.org/W1999173618","https://openalex.org/W2016197810","https://openalex.org/W2016494497","https://openalex.org/W2025607259","https://openalex.org/W2026005846","https://openalex.org/W2061317273","https://openalex.org/W2068835296","https://openalex.org/W2070681743","https://openalex.org/W2071212004","https://openalex.org/W2117418380","https://openalex.org/W2126383014","https://openalex.org/W2135954451","https://openalex.org/W2142635246","https://openalex.org/W2159275794","https://openalex.org/W2167795221","https://openalex.org/W2339801242","https://openalex.org/W3105105114","https://openalex.org/W3105279589","https://openalex.org/W4206469534","https://openalex.org/W4242688646","https://openalex.org/W4243797702","https://openalex.org/W4250038851","https://openalex.org/W4250114020","https://openalex.org/W4300473623","https://openalex.org/W4388534025","https://openalex.org/W6704185022"],"related_works":["https://openalex.org/W2439807930","https://openalex.org/W2009692134","https://openalex.org/W1972271943","https://openalex.org/W2019155478","https://openalex.org/W2024529895","https://openalex.org/W2168175994","https://openalex.org/W1902630399","https://openalex.org/W3120578569","https://openalex.org/W1487412319","https://openalex.org/W1515771853"],"abstract_inverted_index":{"The":[0,47],"problem":[1],"of":[2,28,39,44,54,58,65,93,116],"estimating":[3],"discrete":[4],"time":[5],"stochastic":[6],"processes":[7],"by":[8],"autoregressive":[9,21,96,118],"models":[10],"is":[11,23,76,105],"encountered":[12],"in":[13,37,102,121],"many":[14],"applications.":[15],"In":[16],"most":[17],"practical":[18],"scenarios,":[19],"the":[20,29,34,40,45,51,55,63,69,94,100,110,113,117],"model":[22,70],"derived":[24],"using":[25],"estimated":[26],"values":[27],"covariance":[30,42],"sequence":[31,43,97],"(known":[32],"as":[33,61],"sample":[35],"covariance)":[36],"lieu":[38],"actual":[41],"process.":[46],"present":[48],"paper":[49],"explores":[50],"asymptotic":[52],"behavior":[53],"spectral":[56,91,114],"density":[57,92,115],"such":[59],"approximations,":[60],"both":[62],"number":[64],"samples":[66],"N":[67],"and":[68],"order":[71],"p":[72,84],"approach":[73],"infinity.":[74],"It":[75,104],"shown":[77,107],"that":[78,108],"under":[79,109],"certain":[80],"mild":[81],"assumptions,":[82],"when":[83],"=":[85],"o{N":[86],"<sup":[87,128],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[88,129],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">1/3</sup>":[89],"},":[90],"approximating":[95],"converges":[98,120],"at":[99],"origin":[101],"mean.":[103],"also":[106],"same":[111],"condition,":[112],"approximation":[119],"mean":[122],"with":[123],"respect":[124],"to":[125],"an":[126],"L":[127],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sup>":[130],"norm.":[131]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}