{"id":"https://openalex.org/W2166522845","doi":"https://doi.org/10.1109/tit.1986.1057128","title":"On the estimation of variance for autoregressive and moving average processes (Corresp.)","display_name":"On the estimation of variance for autoregressive and moving average processes (Corresp.)","publication_year":1986,"publication_date":"1986-01-01","ids":{"openalex":"https://openalex.org/W2166522845","doi":"https://doi.org/10.1109/tit.1986.1057128","mag":"2166522845"},"language":"en","primary_location":{"id":"doi:10.1109/tit.1986.1057128","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1986.1057128","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","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/A5027216170","display_name":"B. Porat","orcid":null},"institutions":[{"id":"https://openalex.org/I91203450","display_name":"University of Haifa","ror":"https://ror.org/02f009v59","country_code":"IL","type":"education","lineage":["https://openalex.org/I91203450"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"B. Porat","raw_affiliation_strings":["Department of Electrical Engineering, Haifa, Israel"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Haifa, Israel","institution_ids":["https://openalex.org/I91203450"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006597702","display_name":"B. Friedlander","orcid":"https://orcid.org/0000-0001-5133-2433"},"institutions":[{"id":"https://openalex.org/I4210099960","display_name":"Systems Control (United States)","ror":"https://ror.org/014tted12","country_code":"US","type":"company","lineage":["https://openalex.org/I4210099960"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"B. Friedlander","raw_affiliation_strings":["Saxpy Computer Corporation, Sunnyvale, CA, USA","Systems Control Technology, Inc., Palo Alto, CA, USA"],"affiliations":[{"raw_affiliation_string":"Saxpy Computer Corporation, Sunnyvale, CA, USA","institution_ids":[]},{"raw_affiliation_string":"Systems Control Technology, Inc., Palo Alto, CA, USA","institution_ids":["https://openalex.org/I4210099960"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5027216170"],"corresponding_institution_ids":["https://openalex.org/I91203450"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.28065078,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"32","issue":"1","first_page":"120","last_page":"125"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9905999898910522,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9905999898910522,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11236","display_name":"Control Systems and Identification","score":0.9677000045776367,"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"}},{"id":"https://openalex.org/T10282","display_name":"Financial Risk and Volatility Modeling","score":0.9606000185012817,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/autoregressive-model","display_name":"Autoregressive model","score":0.7430170774459839},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.7278479337692261},{"id":"https://openalex.org/keywords/variance","display_name":"Variance (accounting)","score":0.684941291809082},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.663074791431427},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.6598847508430481},{"id":"https://openalex.org/keywords/sample-variance","display_name":"Sample variance","score":0.5293327569961548},{"id":"https://openalex.org/keywords/bias-of-an-estimator","display_name":"Bias of an estimator","score":0.5236908197402954},{"id":"https://openalex.org/keywords/minimum-variance-unbiased-estimator","display_name":"Minimum-variance unbiased estimator","score":0.5032841563224792},{"id":"https://openalex.org/keywords/variance-based-sensitivity-analysis","display_name":"Variance-based sensitivity analysis","score":0.4714181125164032},{"id":"https://openalex.org/keywords/one-way-analysis-of-variance","display_name":"One-way analysis of variance","score":0.4615713357925415},{"id":"https://openalex.org/keywords/realized-variance","display_name":"Realized variance","score":0.42730361223220825},{"id":"https://openalex.org/keywords/sample","display_name":"Sample (material)","score":0.42190301418304443},{"id":"https://openalex.org/keywords/autoregressive\u2013moving-average-model","display_name":"Autoregressive\u2013moving-average model","score":0.4208011031150818},{"id":"https://openalex.org/keywords/star-model","display_name":"STAR model","score":0.4163059592247009},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.3394986391067505},{"id":"https://openalex.org/keywords/time-series","display_name":"Time series","score":0.2690143585205078},{"id":"https://openalex.org/keywords/autoregressive-integrated-moving-average","display_name":"Autoregressive integrated moving average","score":0.2032671868801117},{"id":"https://openalex.org/keywords/analysis-of-variance","display_name":"Analysis of variance","score":0.20066073536872864},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.04796174168586731}],"concepts":[{"id":"https://openalex.org/C159877910","wikidata":"https://www.wikidata.org/wiki/Q2202883","display_name":"Autoregressive model","level":2,"score":0.7430170774459839},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.7278479337692261},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.684941291809082},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.663074791431427},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.6598847508430481},{"id":"https://openalex.org/C2993021520","wikidata":"https://www.wikidata.org/wiki/Q175199","display_name":"Sample variance","level":3,"score":0.5293327569961548},{"id":"https://openalex.org/C191393472","wikidata":"https://www.wikidata.org/wiki/Q15222032","display_name":"Bias of an estimator","level":4,"score":0.5236908197402954},{"id":"https://openalex.org/C165646398","wikidata":"https://www.wikidata.org/wiki/Q3755281","display_name":"Minimum-variance unbiased estimator","level":3,"score":0.5032841563224792},{"id":"https://openalex.org/C108311543","wikidata":"https://www.wikidata.org/wiki/Q7915756","display_name":"Variance-based sensitivity analysis","level":4,"score":0.4714181125164032},{"id":"https://openalex.org/C152587130","wikidata":"https://www.wikidata.org/wiki/Q7092351","display_name":"One-way analysis of variance","level":3,"score":0.4615713357925415},{"id":"https://openalex.org/C60092789","wikidata":"https://www.wikidata.org/wiki/Q7301291","display_name":"Realized variance","level":3,"score":0.42730361223220825},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.42190301418304443},{"id":"https://openalex.org/C74883015","wikidata":"https://www.wikidata.org/wiki/Q290467","display_name":"Autoregressive\u2013moving-average model","level":3,"score":0.4208011031150818},{"id":"https://openalex.org/C194657046","wikidata":"https://www.wikidata.org/wiki/Q7394685","display_name":"STAR model","level":4,"score":0.4163059592247009},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.3394986391067505},{"id":"https://openalex.org/C151406439","wikidata":"https://www.wikidata.org/wiki/Q186588","display_name":"Time series","level":2,"score":0.2690143585205078},{"id":"https://openalex.org/C24338571","wikidata":"https://www.wikidata.org/wiki/Q2566298","display_name":"Autoregressive integrated moving average","level":3,"score":0.2032671868801117},{"id":"https://openalex.org/C99476002","wikidata":"https://www.wikidata.org/wiki/Q42297","display_name":"Analysis of variance","level":2,"score":0.20066073536872864},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.04796174168586731},{"id":"https://openalex.org/C91602232","wikidata":"https://www.wikidata.org/wiki/Q756115","display_name":"Volatility (finance)","level":2,"score":0.0},{"id":"https://openalex.org/C121955636","wikidata":"https://www.wikidata.org/wiki/Q4116214","display_name":"Accounting","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C43617362","wikidata":"https://www.wikidata.org/wiki/Q170050","display_name":"Chromatography","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.1986.1057128","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1986.1057128","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W2055547925","https://openalex.org/W3015894552","https://openalex.org/W3016210543","https://openalex.org/W3144183905","https://openalex.org/W4229539396"],"related_works":["https://openalex.org/W3004061946","https://openalex.org/W2801330737","https://openalex.org/W2587668322","https://openalex.org/W78698718","https://openalex.org/W2112794329","https://openalex.org/W2891216023","https://openalex.org/W2717948556","https://openalex.org/W2003862733","https://openalex.org/W2741075733","https://openalex.org/W4388952164"],"abstract_inverted_index":{"The":[0],"sample":[1,45,55],"variance":[2,9,46,56,81,87],"is":[3,30,47,65],"commonly":[4],"used":[5],"to":[6,24,49],"estimate":[7],"the":[8,15,19,34,44,54,75,80,86,89],"of":[10,18,36,57,88],"stationary":[11],"time":[12],"series.":[13],"When":[14],"second-order":[16],"statistics":[17],"process":[20,40,61],"are":[21,72],"known":[22],"up":[23],"a":[25,58],"scaling":[26],"factor,":[27],"this":[28],"estimator":[29],"generally":[31,66],"inefficient.":[32],"In":[33],"case":[35],"an":[37,67],"autoregressive":[38],"(AR)":[39],"with":[41,62,79],"unknown":[42,63],"parameters,":[43],"shown":[48],"be":[50],"asymptotically":[51],"efficient.":[52],"However,":[53],"moving-average":[59],"(MA)":[60],"parameters":[64],"inefficient":[68],"estimator.":[69],"Closed-form":[70],"expressions":[71],"derived":[73],"for":[74,85,92],"Cramer-Rao":[76],"hound":[77],"associated":[78],"estimation":[82],"problem":[83],"and":[84,95],"sample-variance":[90],"estimator,":[91],"both":[93],"AR":[94],"MA":[96],"processes.":[97]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
