{"id":"https://openalex.org/W2036096331","doi":"https://doi.org/10.1111/1368-423x.t01-1-00096","title":"An optimal test against a random walk component in a non\u2010orthogonal unobserved components model","display_name":"An optimal test against a random walk component in a non\u2010orthogonal unobserved components model","publication_year":2002,"publication_date":"2002-12-01","ids":{"openalex":"https://openalex.org/W2036096331","doi":"https://doi.org/10.1111/1368-423x.t01-1-00096","mag":"2036096331"},"language":"en","primary_location":{"id":"doi:10.1111/1368-423x.t01-1-00096","doi":"https://doi.org/10.1111/1368-423x.t01-1-00096","is_oa":false,"landing_page_url":"https://doi.org/10.1111/1368-423x.t01-1-00096","pdf_url":null,"source":{"id":"https://openalex.org/S33519306","display_name":"Econometrics Journal","issn_l":"1368-4221","issn":["1368-4221","1368-423X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a-star","anvur-class-a","anvur-scientific","cwts-core","dongbi-b","erih-plus","jufo-2","norway-2","poland-140","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":"The Econometrics Journal","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":null,"display_name":"Ralph W. Bailey","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I79619799","display_name":"University of Birmingham","ror":"https://ror.org/03angcq70","country_code":"GB","type":"education","lineage":["https://openalex.org/I79619799"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Ralph W. Bailey","raw_affiliation_strings":["Department of Economics, University of Birmingham, UK. E\u2010mail: R.W.Bailey@bham.ac.uk; R.Taylor@bham.ac.uk"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Economics, University of Birmingham, UK. E\u2010mail: R.W.Bailey@bham.ac.uk; R.Taylor@bham.ac.uk","institution_ids":["https://openalex.org/I79619799"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072557423","display_name":"Robert Taylor","orcid":"https://orcid.org/0000-0003-0567-0276","observed_orcids":["https://orcid.org/0000-0003-0567-0276"]},"institutions":[{"id":"https://openalex.org/I79619799","display_name":"University of Birmingham","ror":"https://ror.org/03angcq70","country_code":"GB","type":"education","lineage":["https://openalex.org/I79619799"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"A. M. Robert Taylor","raw_affiliation_strings":["Department of Economics, University of Birmingham, UK. E\u2010mail: R.W.Bailey@bham.ac.uk; R.Taylor@bham.ac.uk"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Economics, University of Birmingham, UK. E\u2010mail: R.W.Bailey@bham.ac.uk; R.Taylor@bham.ac.uk","institution_ids":["https://openalex.org/I79619799"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I79619799"],"apc_list":{"value":3384,"currency":"GBP","value_usd":4463},"apc_paid":null,"fwci":1.3989,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.79204512,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"5","issue":"2","first_page":"520","last_page":"532"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13487","display_name":"Statistical and numerical algorithms","score":0.5127000212669373,"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":0.5127000212669373,"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":0.08640000224113464,"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/T10007","display_name":"Monetary Policy and Economic Impact","score":0.06809999793767929,"subfield":{"id":"https://openalex.org/subfields/2000","display_name":"General Economics, Econometrics and 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/random-walks","display_name":"random walks","score":0.6029999852180481},{"id":"https://openalex.org/keywords/unit-root-tests","display_name":"unit root tests","score":0.6349999904632568},{"id":"https://openalex.org/keywords/unobserved-components-model","display_name":"unobserved components model","score":0.7950000166893005},{"id":"https://openalex.org/keywords/locally-best-invariant-test","display_name":"locally best invariant test","score":0.925000011920929},{"id":"https://openalex.org/keywords/asymptotic-distribution","display_name":"asymptotic distribution","score":0.8059999942779541},{"id":"https://openalex.org/keywords/dependent-errors","display_name":"dependent errors","score":0.7310000061988831},{"id":"https://openalex.org/keywords/time-series","display_name":"time series","score":0.39100000262260437}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7612625360488892},{"id":"https://openalex.org/C121194460","wikidata":"https://www.wikidata.org/wiki/Q856741","display_name":"Random walk","level":2,"score":0.7213120460510254},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5458741784095764},{"id":"https://openalex.org/C169857963","wikidata":"https://www.wikidata.org/wiki/Q1461038","display_name":"Test statistic","level":3,"score":0.5329521298408508},{"id":"https://openalex.org/C89128539","wikidata":"https://www.wikidata.org/wiki/Q1949963","display_name":"Statistic","level":2,"score":0.49837636947631836},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.46836721897125244},{"id":"https://openalex.org/C154072304","wikidata":"https://www.wikidata.org/wiki/Q5747218","display_name":"Heterogeneous random walk in one dimension","level":3,"score":0.4611966609954834},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.46083763241767883},{"id":"https://openalex.org/C203763787","wikidata":"https://www.wikidata.org/wiki/Q371029","display_name":"Null (SQL)","level":2,"score":0.4434359073638916},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.44096431136131287},{"id":"https://openalex.org/C36382193","wikidata":"https://www.wikidata.org/wiki/Q7068966","display_name":"Null model","level":2,"score":0.42872336506843567},{"id":"https://openalex.org/C87007009","wikidata":"https://www.wikidata.org/wiki/Q210832","display_name":"Statistical hypothesis testing","level":2,"score":0.37354904413223267},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.21955692768096924},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16220706701278687},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1111/1368-423x.t01-1-00096","doi":"https://doi.org/10.1111/1368-423x.t01-1-00096","is_oa":false,"landing_page_url":"https://doi.org/10.1111/1368-423x.t01-1-00096","pdf_url":null,"source":{"id":"https://openalex.org/S33519306","display_name":"Econometrics Journal","issn_l":"1368-4221","issn":["1368-4221","1368-423X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a-star","anvur-class-a","anvur-scientific","cwts-core","dongbi-b","erih-plus","jufo-2","norway-2","poland-140","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":"The Econometrics Journal","raw_type":"journal-article"},{"id":"pmh:oai:pure.atira.dk:publications/e48ecf25-2716-4f49-bdf5-898a5cd22dae","doi":null,"is_oa":false,"landing_page_url":"https://research.birmingham.ac.uk/portal/en/publications/an-optimal-test-against-a-random-walk-component-in-a-nonorthogonal-unobserved-components-model(e48ecf25-2716-4f49-bdf5-898a5cd22dae).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306402634","display_name":"University of Birmingham Research Portal (University of Birmingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I79619799","host_organization_name":"University of Birmingham","host_organization_lineage":["https://openalex.org/I79619799"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Bailey , R & Taylor , A 2002 , ' An Optimal Test Against a Random Walk Component in a Non-Orthogonal Unobserved Components Model ' , Econometrics Journal , vol. 5 , no. 2 , pp. 520-532 . https://doi.org/10.1111/1368-423X.t01-1-00096","raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[{"score":0.4000000059604645,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W95980050","https://openalex.org/W132604502","https://openalex.org/W605676371","https://openalex.org/W1582394249","https://openalex.org/W1588163064","https://openalex.org/W1604897550","https://openalex.org/W1963640938","https://openalex.org/W1970811061","https://openalex.org/W1971327280","https://openalex.org/W1976725905","https://openalex.org/W1986446727","https://openalex.org/W1999351468","https://openalex.org/W2005013362","https://openalex.org/W2032269423","https://openalex.org/W2049000091","https://openalex.org/W2050853524","https://openalex.org/W2054520318","https://openalex.org/W2062669505","https://openalex.org/W2064288231","https://openalex.org/W2070382733","https://openalex.org/W2073684029","https://openalex.org/W2097580026","https://openalex.org/W2126769996","https://openalex.org/W2133205231","https://openalex.org/W2136518999","https://openalex.org/W2153190668","https://openalex.org/W2241253183","https://openalex.org/W2571446175","https://openalex.org/W2787692114","https://openalex.org/W2904560755","https://openalex.org/W3124750780","https://openalex.org/W4253024587","https://openalex.org/W4307492541","https://openalex.org/W4388071619","https://openalex.org/W4388085717"],"related_works":["https://openalex.org/W2033630974","https://openalex.org/W1968585804","https://openalex.org/W1597743604","https://openalex.org/W3122896853","https://openalex.org/W2316611705","https://openalex.org/W2133977572","https://openalex.org/W746815017","https://openalex.org/W2382807032","https://openalex.org/W2038723108","https://openalex.org/W2605707104"],"abstract_inverted_index":{"In":[0],"this":[1,127],"paper":[2],"we":[3,175],"consider":[4],"the":[5,9,29,32,52,55,67,71,74,85,100,104,120,123,134,140,146,162,178,182,187],"problem":[6,39],"of":[7,22,54,90,122,131,142,172,181,206],"testing":[8],"null":[10,188],"hypothesis":[11],"that":[12,31,66,119,161,177],"a":[13,16,23,35,91,95,155],"series":[14],"has":[15,40],"constant":[17],"level":[18,33,93,98],"(possibly":[19],"as":[20,199],"part":[21],"more":[24],"general":[25],"deterministic":[26],"mean)":[27],"against":[28,94],"alternative":[30],"follows":[34],"random":[36,58,75,96,107],"walk.":[37],"This":[38,63,153],"previously":[41,137],"been":[42],"studied":[43],"by,":[44],"inter":[45],"alia,":[46],"Nyblom":[47],"and":[48,70,106,189,213],"M\u00e4kel\u00e4inen":[49],"(1983)":[50],"in":[51,99,126],"context":[53],"orthogonal":[56],"Gaussian":[57],"walk":[59,76,97,108],"plus":[60],"noise":[61,68,105],"model.":[62],"model":[64],"postulates":[65],"component":[69],"innovations":[72],"to":[73,211,215],"are":[77,110,209,220],"uncorrelated.":[78],"We":[79,117],"generalize":[80],"their":[81],"work":[82],"by":[83],"deriving":[84],"locally":[86,147,163],"best":[87],"invariant":[88],"test":[89,125,135,149,165],"fixed":[92],"non\u2010orthogonal":[101],"case.":[102],"Here":[103],"components":[109],"contemporaneously":[111],"correlated":[112],"with":[113,217],"correlation":[114],"coefficient":[115],"\u03c1.":[116,152,173],"demonstrate":[118],"form":[121],"optimal":[124,148,164],"setting":[128],"is":[129,154],"independent":[130],"\u03c1;":[132],"i.e.":[133],"statistic":[136,184],"derived":[138],"for":[139,150],"case":[141],"\u03c1=":[143,201],"0":[144],"remains":[145],"all":[151],"very":[156],"useful":[157],"result:":[158],"it":[159],"states":[160],"may":[166],"be":[167],"achieved":[168],"without":[169],"prior":[170],"knowledge":[171],"Moreover,":[174],"show":[176],"limiting":[179],"distribution":[180],"resulting":[183],"under":[185],"both":[186],"local":[190],"alternatives":[191],"does":[192],"not":[193],"depend":[194],"on":[195],"\u03c1,":[196],"behaving":[197],"exactly":[198],"if":[200],"0.":[202],"Finite":[203],"sample":[204],"simulations":[205],"these":[207],"effects":[208],"provided":[210],"illustrate":[212],"generalizations":[214],"models":[216],"dependent":[218],"errors":[219],"considered.":[221]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-10-14T16:39:01.820549","created_date":"2025-10-10T00:00:00"}
