{"id":"https://openalex.org/W2904366992","doi":"https://doi.org/10.1111/j.2517-6161.1964.tb00547.x","title":"Estimation of the Spectral Density Function in the Presence of Harmonic Components","display_name":"Estimation of the Spectral Density Function in the Presence of Harmonic Components","publication_year":1964,"publication_date":"1964-01-01","ids":{"openalex":"https://openalex.org/W2904366992","doi":"https://doi.org/10.1111/j.2517-6161.1964.tb00547.x","mag":"2904366992"},"language":"en","primary_location":{"id":"doi:10.1111/j.2517-6161.1964.tb00547.x","doi":"https://doi.org/10.1111/j.2517-6161.1964.tb00547.x","is_oa":false,"landing_page_url":"https://doi.org/10.1111/j.2517-6161.1964.tb00547.x","pdf_url":null,"source":{"id":"https://openalex.org/S145009937","display_name":"Journal of the Royal Statistical Society Series B (Statistical Methodology)","issn_l":"1369-7412","issn":["1369-7412","1467-9868"],"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-1","norway-2","poland-200","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the Royal Statistical Society Series B: Statistical Methodology","raw_type":"journal-article"},"volume":null,"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/A5009815533","display_name":"Mark Priestley","orcid":"https://orcid.org/0000-0003-3039-9043","observed_orcids":["https://orcid.org/0000-0003-3039-9043"]},"institutions":[{"id":"https://openalex.org/I28407311","display_name":"University of Manchester","ror":"https://ror.org/027m9bs27","country_code":"GB","type":"education","lineage":["https://openalex.org/I28407311"]},{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["GB","US"],"is_corresponding":true,"raw_author_name":"M. B. Priestley","raw_affiliation_strings":["Stanford University and University of Manchester"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Stanford University and University of Manchester","institution_ids":["https://openalex.org/I28407311","https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5009815533"],"corresponding_institution_ids":["https://openalex.org/I28407311","https://openalex.org/I97018004"],"apc_list":{"value":2621,"currency":"GBP","value_usd":3456},"apc_paid":null,"fwci":0.4821,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.7020202,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"26","issue":"1","first_page":"123","last_page":"132"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13487","display_name":"Statistical and numerical algorithms","score":0.6937999725341797,"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"}},"topics":[{"id":"https://openalex.org/T13487","display_name":"Statistical and numerical algorithms","score":0.6937999725341797,"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"}},{"id":"https://openalex.org/T12205","display_name":"Time Series Analysis and Forecasting","score":0.15299999713897705,"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/T11911","display_name":"Spatial and Panel Data Analysis","score":0.021700000390410423,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"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/spectral-density-estimation","display_name":"spectral density estimation","score":0.9779999852180481},{"id":"https://openalex.org/keywords/harmonics","display_name":"harmonics","score":0.878000020980835},{"id":"https://openalex.org/keywords/linear-processes","display_name":"linear processes","score":0.6769999861717224},{"id":"https://openalex.org/keywords/stationary-processes","display_name":"stationary processes","score":0.6890000104904175},{"id":"https://openalex.org/keywords/continuous-spectrum","display_name":"continuous spectrum","score":0.4729999899864197}],"concepts":[{"id":"https://openalex.org/C88271906","wikidata":"https://www.wikidata.org/wiki/Q786973","display_name":"Autocovariance","level":3,"score":0.9947976469993591},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6855834126472473},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.6074382662773132},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.6033280491828918},{"id":"https://openalex.org/C168110828","wikidata":"https://www.wikidata.org/wiki/Q1331626","display_name":"Spectral density","level":2,"score":0.599956750869751},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.5554220676422119},{"id":"https://openalex.org/C30049272","wikidata":"https://www.wikidata.org/wiki/Q6555326","display_name":"Spectral density estimation","level":3,"score":0.5245481133460999},{"id":"https://openalex.org/C131770355","wikidata":"https://www.wikidata.org/wiki/Q876215","display_name":"Harmonic analysis","level":2,"score":0.44502872228622437},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.384446918964386},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36087456345558167},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.21563515067100525},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.20360207557678223},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06619173288345337},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1111/j.2517-6161.1964.tb00547.x","doi":"https://doi.org/10.1111/j.2517-6161.1964.tb00547.x","is_oa":false,"landing_page_url":"https://doi.org/10.1111/j.2517-6161.1964.tb00547.x","pdf_url":null,"source":{"id":"https://openalex.org/S145009937","display_name":"Journal of the Royal Statistical Society Series B (Statistical Methodology)","issn_l":"1369-7412","issn":["1369-7412","1467-9868"],"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-1","norway-2","poland-200","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the Royal Statistical Society Series B: Statistical Methodology","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1991196564","https://openalex.org/W2049156204","https://openalex.org/W2051938986","https://openalex.org/W2064737301","https://openalex.org/W2082873187","https://openalex.org/W2090215089","https://openalex.org/W2092800390","https://openalex.org/W2796529750","https://openalex.org/W2903656127","https://openalex.org/W2904498125","https://openalex.org/W4235510040","https://openalex.org/W4294576247","https://openalex.org/W6648193942"],"related_works":["https://openalex.org/W2064515180","https://openalex.org/W4251726294","https://openalex.org/W1993505442","https://openalex.org/W2564659261","https://openalex.org/W4294006382","https://openalex.org/W2181164662","https://openalex.org/W2186403646","https://openalex.org/W3014721535","https://openalex.org/W49922925","https://openalex.org/W2481210175"],"abstract_inverted_index":{"Summary":[0],"Consider":[1],"a":[2,16,20,26],"stationary":[3],"process":[4,18],"of":[5,29,36,42,53,61,86],"the":[6,38,50,57,66,72,77,83,90],"form":[7,65],"Xt":[8,87],"=":[9],"Yt":[10,14,54],"+":[11],"Zt,":[12],"where":[13],"is":[15,25],"linear":[17],"with":[19],"continuous":[21],"spectrum,":[22],"and":[23,63],"Zt":[24],"finite":[27],"sum":[28],"harmonic":[30],"components.":[31],"We":[32],"discuss":[33],"two":[34],"methods":[35],"estimating":[37],"spectral":[39,78],"density":[40,79],"function":[41,52,60,80,85],"Yt.":[43],"In":[44,71],"one":[45],"method":[46],"we":[47,75],"first":[48],"estimate":[49,76],"autocovariance":[51,59,84],"by":[55,88],"\u201ccorrecting\u201d":[56],"sample":[58],"Xt,":[62],"then":[64],"usual":[67],"\u201csmoothed\u201d":[68],"Fourier":[69],"transform.":[70],"other":[73],"approach,":[74],"directly":[81],"from":[82],"using":[89],"\u201cdouble":[91],"weight":[92],"function\u201d":[93],"technique.":[94]},"counts_by_year":[{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-10-12T09:40:04.860316","created_date":"2025-10-10T00:00:00"}