{"id":"https://openalex.org/W2468452228","doi":"https://doi.org/10.1109/tsp.2016.2599503","title":"A Widely Linear Complex Autoregressive Process of Order One","display_name":"A Widely Linear Complex Autoregressive Process of Order One","publication_year":2016,"publication_date":"2016-08-10","ids":{"openalex":"https://openalex.org/W2468452228","doi":"https://doi.org/10.1109/tsp.2016.2599503","mag":"2468452228"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2016.2599503","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2016.2599503","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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 Signal Processing","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1511.04128","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5026098176","display_name":"Adam M. Sykulski","orcid":"https://orcid.org/0000-0002-5564-3674"},"institutions":[{"id":"https://openalex.org/I45129253","display_name":"University College London","ror":"https://ror.org/02jx3x895","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I45129253"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Adam M. Sykulski","raw_affiliation_strings":["Department of Statistical Science, University College London, London, U.K","Department of Statistical Science, University College London, Gower Street, London WC1E 6BT, UK"],"affiliations":[{"raw_affiliation_string":"Department of Statistical Science, University College London, London, U.K","institution_ids":["https://openalex.org/I45129253"]},{"raw_affiliation_string":"Department of Statistical Science, University College London, Gower Street, London WC1E 6BT, UK","institution_ids":["https://openalex.org/I45129253"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083945023","display_name":"Sofia C. Olhede","orcid":"https://orcid.org/0000-0003-0061-227X"},"institutions":[{"id":"https://openalex.org/I45129253","display_name":"University College London","ror":"https://ror.org/02jx3x895","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I45129253"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Sofia C. Olhede","raw_affiliation_strings":["Alan Turing Institute, London, U.K","Department of Statistical Science, University College London, Gower Street, London, U.K","Department of Statistical Science, University College London, Gower Street, London WC1E 6BT, UK"],"affiliations":[{"raw_affiliation_string":"Alan Turing Institute, London, U.K","institution_ids":[]},{"raw_affiliation_string":"Department of Statistical Science, University College London, Gower Street, London, U.K","institution_ids":[]},{"raw_affiliation_string":"Department of Statistical Science, University College London, Gower Street, London WC1E 6BT, UK","institution_ids":["https://openalex.org/I45129253"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000657624","display_name":"Jonathan M. Lilly","orcid":"https://orcid.org/0000-0001-5651-7496"},"institutions":[{"id":"https://openalex.org/I45129253","display_name":"University College London","ror":"https://ror.org/02jx3x895","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I45129253"]},{"id":"https://openalex.org/I4210144897","display_name":"Northwest Research Associates","ror":"https://ror.org/0583jne22","country_code":"US","type":"facility","lineage":["https://openalex.org/I4210144897"]}],"countries":["GB","US"],"is_corresponding":false,"raw_author_name":"Jonathan M. Lilly","raw_affiliation_strings":["NorthWest Research Associates, Bellevue, WA, USA","Department of Statistical Science, University College London, Gower Street, London WC1E 6BT, UK"],"affiliations":[{"raw_affiliation_string":"NorthWest Research Associates, Bellevue, WA, USA","institution_ids":["https://openalex.org/I4210144897"]},{"raw_affiliation_string":"Department of Statistical Science, University College London, Gower Street, London WC1E 6BT, UK","institution_ids":["https://openalex.org/I45129253"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5026098176"],"corresponding_institution_ids":["https://openalex.org/I45129253"],"apc_list":null,"apc_paid":null,"fwci":2.703,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.93606088,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"64","issue":"23","first_page":"6200","last_page":"6210"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9894999861717224,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9894999861717224,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T10534","display_name":"Structural Health Monitoring Techniques","score":0.9771000146865845,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural 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/T11447","display_name":"Blind Source Separation Techniques","score":0.9693999886512756,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/autoregressive-model","display_name":"Autoregressive model","score":0.9151536226272583},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.6331717371940613},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.5782155990600586},{"id":"https://openalex.org/keywords/bivariate-analysis","display_name":"Bivariate analysis","score":0.5373628735542297},{"id":"https://openalex.org/keywords/frequency-domain","display_name":"Frequency domain","score":0.5083779692649841},{"id":"https://openalex.org/keywords/star-model","display_name":"STAR model","score":0.49895167350769043},{"id":"https://openalex.org/keywords/autocorrelation","display_name":"Autocorrelation","score":0.4879433512687683},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.47521334886550903},{"id":"https://openalex.org/keywords/nonlinear-autoregressive-exogenous-model","display_name":"Nonlinear autoregressive exogenous model","score":0.472206175327301},{"id":"https://openalex.org/keywords/continuous-time-stochastic-process","display_name":"Continuous-time stochastic process","score":0.4719963073730469},{"id":"https://openalex.org/keywords/stochastic-modelling","display_name":"Stochastic modelling","score":0.447139173746109},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.445444256067276},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4381256401538849},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38149338960647583},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.379489541053772},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3791637420654297},{"id":"https://openalex.org/keywords/autoregressive-integrated-moving-average","display_name":"Autoregressive integrated moving average","score":0.3236057162284851},{"id":"https://openalex.org/keywords/time-series","display_name":"Time series","score":0.23910394310951233},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.217350035905838},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.14910471439361572}],"concepts":[{"id":"https://openalex.org/C159877910","wikidata":"https://www.wikidata.org/wiki/Q2202883","display_name":"Autoregressive model","level":2,"score":0.9151536226272583},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.6331717371940613},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.5782155990600586},{"id":"https://openalex.org/C64341305","wikidata":"https://www.wikidata.org/wiki/Q4919225","display_name":"Bivariate analysis","level":2,"score":0.5373628735542297},{"id":"https://openalex.org/C19118579","wikidata":"https://www.wikidata.org/wiki/Q786423","display_name":"Frequency domain","level":2,"score":0.5083779692649841},{"id":"https://openalex.org/C194657046","wikidata":"https://www.wikidata.org/wiki/Q7394685","display_name":"STAR model","level":4,"score":0.49895167350769043},{"id":"https://openalex.org/C5297727","wikidata":"https://www.wikidata.org/wiki/Q786970","display_name":"Autocorrelation","level":2,"score":0.4879433512687683},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.47521334886550903},{"id":"https://openalex.org/C42536954","wikidata":"https://www.wikidata.org/wiki/Q7049462","display_name":"Nonlinear autoregressive exogenous model","level":3,"score":0.472206175327301},{"id":"https://openalex.org/C158535547","wikidata":"https://www.wikidata.org/wiki/Q5165437","display_name":"Continuous-time stochastic process","level":3,"score":0.4719963073730469},{"id":"https://openalex.org/C127491075","wikidata":"https://www.wikidata.org/wiki/Q7617825","display_name":"Stochastic modelling","level":2,"score":0.447139173746109},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.445444256067276},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4381256401538849},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38149338960647583},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.379489541053772},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3791637420654297},{"id":"https://openalex.org/C24338571","wikidata":"https://www.wikidata.org/wiki/Q2566298","display_name":"Autoregressive integrated moving average","level":3,"score":0.3236057162284851},{"id":"https://openalex.org/C151406439","wikidata":"https://www.wikidata.org/wiki/Q186588","display_name":"Time series","level":2,"score":0.23910394310951233},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.217350035905838},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.14910471439361572},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1109/tsp.2016.2599503","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2016.2599503","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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 Signal Processing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1511.04128","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1511.04128","pdf_url":"https://arxiv.org/pdf/1511.04128","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:eprints.lancs.ac.uk:87318","is_oa":false,"landing_page_url":"https://eprints.lancs.ac.uk/id/eprint/87318/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401916","display_name":"Lancaster EPrints (Lancaster University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67415387","host_organization_name":"Lancaster University","host_organization_lineage":["https://openalex.org/I67415387"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"},{"id":"pmh:oai:eprints.ucl.ac.uk.OAI2:1494954","is_oa":false,"landing_page_url":"https://discovery.ucl.ac.uk/id/eprint/1494954/","pdf_url":null,"source":{"id":"https://openalex.org/S4306400024","display_name":"UCL Discovery (University College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45129253","host_organization_name":"University College London","host_organization_lineage":["https://openalex.org/I45129253"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"   IEEE Transactions on Signal Processing , 64  (23)   pp. 6200-6210.   (2016)      ","raw_type":"Article"},{"id":"pmh:oai:spiral.imperial.ac.uk:10044/1/98095","is_oa":false,"landing_page_url":"http://hdl.handle.net/10044/1/98095","pdf_url":null,"source":{"id":"https://openalex.org/S4306401396","display_name":"Spiral (Imperial College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I47508984","host_organization_name":"Imperial College London","host_organization_lineage":["https://openalex.org/I47508984"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"6210","raw_type":"Journal Article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1511.04128","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1511.04128","pdf_url":"https://arxiv.org/pdf/1511.04128","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1179212010","display_name":null,"funder_award_id":"EP/I005250/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G2013446834","display_name":null,"funder_award_id":"682172","funder_id":"https://openalex.org/F4320334678","funder_display_name":"European Research Council"},{"id":"https://openalex.org/G378314651","display_name":"High Dimensional Models for Multivariate Time Series Analysis","funder_award_id":"EP/I005250/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G4569133667","display_name":"Whittle Estimation for Lagrangian Trajectories - Regional Analysis and Environmental Consequences","funder_award_id":"EP/L025744/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G5633173029","display_name":null,"funder_award_id":"EP/L025744/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"},{"id":"https://openalex.org/F4320334678","display_name":"European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W140860961","https://openalex.org/W639989723","https://openalex.org/W1595456774","https://openalex.org/W1857858871","https://openalex.org/W1877665914","https://openalex.org/W1982176366","https://openalex.org/W1988423005","https://openalex.org/W1997927852","https://openalex.org/W2007729040","https://openalex.org/W2013448945","https://openalex.org/W2038421291","https://openalex.org/W2041043544","https://openalex.org/W2049611406","https://openalex.org/W2058087147","https://openalex.org/W2063388524","https://openalex.org/W2067489830","https://openalex.org/W2090267260","https://openalex.org/W2093149331","https://openalex.org/W2094250531","https://openalex.org/W2096844050","https://openalex.org/W2100506777","https://openalex.org/W2110065044","https://openalex.org/W2110210567","https://openalex.org/W2124171390","https://openalex.org/W2131026060","https://openalex.org/W2139996618","https://openalex.org/W2142224505","https://openalex.org/W2155849898","https://openalex.org/W2156105064","https://openalex.org/W2157228636","https://openalex.org/W2158436791","https://openalex.org/W2159071216","https://openalex.org/W2161735865","https://openalex.org/W2169430226","https://openalex.org/W2400965166","https://openalex.org/W2408117717","https://openalex.org/W2975023231","https://openalex.org/W2987957311","https://openalex.org/W3099264590","https://openalex.org/W3146166473","https://openalex.org/W4211251910","https://openalex.org/W4241115065","https://openalex.org/W4247677155","https://openalex.org/W4297069708","https://openalex.org/W6665278033","https://openalex.org/W6713039846","https://openalex.org/W6714150190"],"related_works":["https://openalex.org/W4366145459","https://openalex.org/W2019155478","https://openalex.org/W2041578667","https://openalex.org/W304218021","https://openalex.org/W3123153965","https://openalex.org/W4287185323","https://openalex.org/W2111126525","https://openalex.org/W2154965898","https://openalex.org/W2098152933","https://openalex.org/W2888652631"],"abstract_inverted_index":{"We":[0,65,83,99],"propose":[1],"a":[2,16,20,27,45],"simple":[3],"stochastic":[4,42,59],"process":[5,14,33,49,106],"for":[6,68],"modeling":[7,60],"improper":[8],"or":[9],"noncircular":[10],"complex-valued":[11,21],"signals.":[12,117],"The":[13,48],"is":[15,50,54],"natural":[17],"extension":[18],"of":[19,74,80,104],"autoregressive":[22,30],"process,":[23],"extended":[24],"to":[25,40],"include":[26],"widely":[28],"linear":[29],"term.":[31],"This":[32],"can":[34,88],"then":[35],"capture":[36],"elliptical,":[37],"as":[38],"opposed":[39],"circular,":[41],"oscillations":[43,110],"in":[44,62,93,107,115],"bivariate":[46],"signal.":[47],"order":[51],"one":[52],"and":[53,70,77,96],"more":[55],"parsimonious":[56],"than":[57],"alternative":[58],"approaches":[61],"the":[63,72,75,94,101,105],"literature.":[64],"provide":[66],"conditions":[67],"stationarity,":[69],"derive":[71],"form":[73],"covariance":[76],"relation":[78],"sequence":[79],"this":[81],"model.":[82],"describe":[84],"how":[85],"parameter":[86],"estimation":[87],"be":[89],"efficiently":[90],"performed":[91],"both":[92],"time":[95],"frequency":[97],"domain.":[98],"demonstrate":[100],"practical":[102],"utility":[103],"capturing":[108],"elliptical":[109],"that":[111],"are":[112],"naturally":[113],"present":[114],"seismic":[116]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":4}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}
