{"id":"https://openalex.org/W2003402295","doi":"https://doi.org/10.1214/aos/1176343415","title":"The Asymptotic Distribution of Serial Covariances","display_name":"The Asymptotic Distribution of Serial Covariances","publication_year":1976,"publication_date":"1976-03-01","ids":{"openalex":"https://openalex.org/W2003402295","doi":"https://doi.org/10.1214/aos/1176343415","mag":"2003402295"},"language":"en","primary_location":{"id":"doi:10.1214/aos/1176343415","doi":"https://doi.org/10.1214/aos/1176343415","is_oa":true,"landing_page_url":"https://doi.org/10.1214/aos/1176343415","pdf_url":"https://projecteuclid.org/journals/annals-of-statistics/volume-4/issue-2/The-Asymptotic-Distribution-of-Serial-Covariances/10.1214/aos/1176343415.pdf","source":{"id":"https://openalex.org/S119757635","display_name":"The Annals of Statistics","issn_l":"0090-5364","issn":["0090-5364","2168-8966"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a-star","anvur-class-a","anvur-scientific","cwts-core","dongbi-a","doyens","jufo-3","ki-jl-2","norway-2","poland-200","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319881","host_organization_name":"Institute of Mathematical Statistics","host_organization_lineage":["https://openalex.org/P4310319881"],"host_organization_lineage_names":["Institute of Mathematical Statistics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Annals of Statistics","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://projecteuclid.org/journals/annals-of-statistics/volume-4/issue-2/The-Asymptotic-Distribution-of-Serial-Covariances/10.1214/aos/1176343415.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016777339","display_name":"E. J. Hannan","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"E. J. Hannan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5016777339"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.2753,"has_fulltext":false,"cited_by_count":100,"citation_normalized_percentile":{"value":0.77275265,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"4","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13500","display_name":"Probability and Statistical Research","score":0.39480000734329224,"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/T13500","display_name":"Probability and Statistical Research","score":0.39480000734329224,"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/T12205","display_name":"Time Series Analysis and Forecasting","score":0.27250000834465027,"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/T13487","display_name":"Statistical and numerical algorithms","score":0.11500000208616257,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/central-limit-theorem","display_name":"central limit theorem","score":0.9179999828338623},{"id":"https://openalex.org/keywords/asymptotic-distribution","display_name":"asymptotic distribution","score":0.8489999771118164},{"id":"https://openalex.org/keywords/power-spectrum","display_name":"power spectrum","score":0.6389999985694885},{"id":"https://openalex.org/keywords/sample-covariance","display_name":"sample covariance","score":0.3440000116825104}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9265058040618896},{"id":"https://openalex.org/C166785042","wikidata":"https://www.wikidata.org/wiki/Q190391","display_name":"Central limit theorem","level":2,"score":0.6912322044372559},{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.6375539302825928},{"id":"https://openalex.org/C65778772","wikidata":"https://www.wikidata.org/wiki/Q12345341","display_name":"Asymptotic distribution","level":3,"score":0.5108330249786377},{"id":"https://openalex.org/C176181172","wikidata":"https://www.wikidata.org/wiki/Q3490301","display_name":"Nondeterministic algorithm","level":2,"score":0.49316471815109253},{"id":"https://openalex.org/C151424130","wikidata":"https://www.wikidata.org/wiki/Q17123911","display_name":"Stationary ergodic process","level":4,"score":0.4800049662590027},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.47824209928512573},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.47315487265586853},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.4488056004047394},{"id":"https://openalex.org/C18436578","wikidata":"https://www.wikidata.org/wiki/Q7604346","display_name":"Stationary sequence","level":3,"score":0.4456098675727844},{"id":"https://openalex.org/C88271906","wikidata":"https://www.wikidata.org/wiki/Q786973","display_name":"Autocovariance","level":3,"score":0.4235472083091736},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.41516003012657166},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.27415189146995544},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.27137163281440735},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27102571725845337},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.13762730360031128},{"id":"https://openalex.org/C115667082","wikidata":"https://www.wikidata.org/wiki/Q4200518","display_name":"Invariant measure","level":3,"score":0.09267076849937439},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.087227463722229},{"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":2,"locations":[{"id":"doi:10.1214/aos/1176343415","doi":"https://doi.org/10.1214/aos/1176343415","is_oa":true,"landing_page_url":"https://doi.org/10.1214/aos/1176343415","pdf_url":"https://projecteuclid.org/journals/annals-of-statistics/volume-4/issue-2/The-Asymptotic-Distribution-of-Serial-Covariances/10.1214/aos/1176343415.pdf","source":{"id":"https://openalex.org/S119757635","display_name":"The Annals of Statistics","issn_l":"0090-5364","issn":["0090-5364","2168-8966"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a-star","anvur-class-a","anvur-scientific","cwts-core","dongbi-a","doyens","jufo-3","ki-jl-2","norway-2","poland-200","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319881","host_organization_name":"Institute of Mathematical Statistics","host_organization_lineage":["https://openalex.org/P4310319881"],"host_organization_lineage_names":["Institute of Mathematical Statistics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Annals of Statistics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.aos/1176343415","doi":null,"is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.aos/1176343415","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1214/aos/1176343415","doi":"https://doi.org/10.1214/aos/1176343415","is_oa":true,"landing_page_url":"https://doi.org/10.1214/aos/1176343415","pdf_url":"https://projecteuclid.org/journals/annals-of-statistics/volume-4/issue-2/The-Asymptotic-Distribution-of-Serial-Covariances/10.1214/aos/1176343415.pdf","source":{"id":"https://openalex.org/S119757635","display_name":"The Annals of Statistics","issn_l":"0090-5364","issn":["0090-5364","2168-8966"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a-star","anvur-class-a","anvur-scientific","cwts-core","dongbi-a","doyens","jufo-3","ki-jl-2","norway-2","poland-200","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319881","host_organization_name":"Institute of Mathematical Statistics","host_organization_lineage":["https://openalex.org/P4310319881"],"host_organization_lineage_names":["Institute of Mathematical Statistics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Annals of Statistics","raw_type":"journal-article"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2003402295.pdf","grobid_xml":"https://content.openalex.org/works/W2003402295.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1986570523","https://openalex.org/W2054957878","https://openalex.org/W2370545062","https://openalex.org/W1531222062","https://openalex.org/W2035603697","https://openalex.org/W2021796436","https://openalex.org/W2951918876","https://openalex.org/W4251726294","https://openalex.org/W2094729362","https://openalex.org/W1965944255"],"abstract_inverted_index":{"A":[0],"central":[1],"limit":[2],"theorem":[3,41],"is":[4,42],"proved":[5],"for":[6,27,39],"the":[7,40,45],"sample":[8],"serial":[9],"covariances":[10],"of":[11,30],"an":[12],"ergodic,":[13],"stationary,":[14],"purely":[15],"nondeterministic":[16],"process":[17],"whose":[18],"linear":[19],"innovations":[20],"have":[21],"their":[22],"first":[23],"four":[24],"moments":[25],"as":[26],"a":[28],"sequence":[29],"independent":[31],"random":[32],"variables.":[33],"The":[34],"necessary":[35],"and":[36],"sufficient":[37],"condition":[38],"then":[43],"that":[44],"spectra":[46],"be":[47],"square":[48],"integrable.":[49]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2026-10-12T09:40:04.860316","created_date":"2025-10-10T00:00:00"}
