{"id":"https://openalex.org/W4381889845","doi":"https://doi.org/10.1007/s00180-023-01377-x","title":"Multi-step estimators and shrinkage effect in time series models","display_name":"Multi-step estimators and shrinkage effect in time series models","publication_year":2023,"publication_date":"2023-06-24","ids":{"openalex":"https://openalex.org/W4381889845","doi":"https://doi.org/10.1007/s00180-023-01377-x"},"language":"en","primary_location":{"id":"doi:10.1007/s00180-023-01377-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00180-023-01377-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00180-023-01377-x.pdf","source":{"id":"https://openalex.org/S8500805","display_name":"Computational Statistics","issn_l":"0943-4062","issn":["0943-4062","1613-9658"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Statistics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00180-023-01377-x.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001798041","display_name":"Ivan Svetunkov","orcid":"https://orcid.org/0000-0001-7826-0281"},"institutions":[{"id":"https://openalex.org/I67415387","display_name":"Lancaster University","ror":"https://ror.org/04f2nsd36","country_code":"GB","type":"education","lineage":["https://openalex.org/I67415387"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Ivan Svetunkov","raw_affiliation_strings":["Centre for Marketing Analytics and Forecasting, Lancaster University Management School, Lancaster, LA1 4YX, UK","Department of Management Science, Lancaster University Management School, Lancaster, Lancashire, LA1 4YX, UK"],"raw_orcid":"https://orcid.org/0000-0001-7826-0281","affiliations":[{"raw_affiliation_string":"Centre for Marketing Analytics and Forecasting, Lancaster University Management School, Lancaster, LA1 4YX, UK","institution_ids":["https://openalex.org/I67415387"]},{"raw_affiliation_string":"Department of Management Science, Lancaster University Management School, Lancaster, Lancashire, LA1 4YX, UK","institution_ids":["https://openalex.org/I67415387"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064340262","display_name":"Nikolaos Kourentzes","orcid":"https://orcid.org/0000-0003-0211-5218"},"institutions":[{"id":"https://openalex.org/I205158640","display_name":"University of Sk\u00f6vde","ror":"https://ror.org/051mrsz47","country_code":"SE","type":"education","lineage":["https://openalex.org/I205158640"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Nikolaos Kourentzes","raw_affiliation_strings":["Sk\u00f6vde Artificial Intelligence Lab, School of Informatics, University of Sk\u00f6vde, Sk\u00f6vde, Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Sk\u00f6vde Artificial Intelligence Lab, School of Informatics, University of Sk\u00f6vde, Sk\u00f6vde, Sweden","institution_ids":["https://openalex.org/I205158640"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5075851671","display_name":"Rebecca Killick","orcid":"https://orcid.org/0000-0003-0583-3960"},"institutions":[{"id":"https://openalex.org/I67415387","display_name":"Lancaster University","ror":"https://ror.org/04f2nsd36","country_code":"GB","type":"education","lineage":["https://openalex.org/I67415387"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Rebecca Killick","raw_affiliation_strings":["Department of Mathematics and Statistics, Lancaster University, Lancaster, LA1 4YF, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Lancaster University, Lancaster, LA1 4YF, UK","institution_ids":["https://openalex.org/I67415387"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5001798041"],"corresponding_institution_ids":["https://openalex.org/I67415387"],"apc_list":{"value":3090,"currency":"USD","value_usd":3090},"apc_paid":{"value":3090,"currency":"USD","value_usd":3090},"fwci":1.3504,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.80932403,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"39","issue":"3","first_page":"1203","last_page":"1239"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11918","display_name":"Forecasting Techniques and Applications","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11918","display_name":"Forecasting Techniques and Applications","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11871","display_name":"Advanced Statistical Methods and Models","score":0.9904000163078308,"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/T10282","display_name":"Financial Risk and Volatility Modeling","score":0.9890999794006348,"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/estimator","display_name":"Estimator","score":0.8922157287597656},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.688072919845581},{"id":"https://openalex.org/keywords/univariate","display_name":"Univariate","score":0.6836006045341492},{"id":"https://openalex.org/keywords/trace","display_name":"TRACE (psycholinguistics)","score":0.5393343567848206},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.537514865398407},{"id":"https://openalex.org/keywords/shrinkage","display_name":"Shrinkage","score":0.5256273150444031},{"id":"https://openalex.org/keywords/mean-squared-error","display_name":"Mean squared error","score":0.4394156336784363},{"id":"https://openalex.org/keywords/time-series","display_name":"Time series","score":0.4385794997215271},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.37043577432632446},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33083468675613403},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.30996429920196533},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3080572783946991},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.2026776373386383},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.179190993309021}],"concepts":[{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.8922157287597656},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.688072919845581},{"id":"https://openalex.org/C199163554","wikidata":"https://www.wikidata.org/wiki/Q1681619","display_name":"Univariate","level":3,"score":0.6836006045341492},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.5393343567848206},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.537514865398407},{"id":"https://openalex.org/C180145272","wikidata":"https://www.wikidata.org/wiki/Q7504144","display_name":"Shrinkage","level":2,"score":0.5256273150444031},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.4394156336784363},{"id":"https://openalex.org/C151406439","wikidata":"https://www.wikidata.org/wiki/Q186588","display_name":"Time series","level":2,"score":0.4385794997215271},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.37043577432632446},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33083468675613403},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.30996429920196533},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3080572783946991},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.2026776373386383},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.179190993309021},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","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":4,"locations":[{"id":"doi:10.1007/s00180-023-01377-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00180-023-01377-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00180-023-01377-x.pdf","source":{"id":"https://openalex.org/S8500805","display_name":"Computational Statistics","issn_l":"0943-4062","issn":["0943-4062","1613-9658"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Statistics","raw_type":"journal-article"},{"id":"pmh:oai:DiVA.org:his-22982","is_oa":true,"landing_page_url":"http://urn.kb.se/resolve?urn=urn:nbn:se:his:diva-22982","pdf_url":null,"source":{"id":"https://openalex.org/S4306401559","display_name":"KTH Publication Database DiVA (KTH Royal Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I86987016","host_organization_name":"KTH Royal Institute of Technology","host_organization_lineage":["https://openalex.org/I86987016"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:RePEc:spr:compst:v:39:y:2024:i:3:d:10.1007_s00180-023-01377-x","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s00180-023-01377-x","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:eprints.lancs.ac.uk:204584","is_oa":false,"landing_page_url":"https://eprints.lancs.ac.uk/id/eprint/204584/","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":null,"raw_type":"Journal Article"}],"best_oa_location":{"id":"doi:10.1007/s00180-023-01377-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00180-023-01377-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00180-023-01377-x.pdf","source":{"id":"https://openalex.org/S8500805","display_name":"Computational Statistics","issn_l":"0943-4062","issn":["0943-4062","1613-9658"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Statistics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2117203297","display_name":null,"funder_award_id":"EP/T021020/1","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"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4381889845.pdf","grobid_xml":"https://content.openalex.org/works/W4381889845.grobid-xml"},"referenced_works_count":43,"referenced_works":["https://openalex.org/W95980050","https://openalex.org/W105632781","https://openalex.org/W1601914933","https://openalex.org/W1709435319","https://openalex.org/W1984717679","https://openalex.org/W1985815014","https://openalex.org/W1990178215","https://openalex.org/W1995730172","https://openalex.org/W2008192499","https://openalex.org/W2034767804","https://openalex.org/W2053375504","https://openalex.org/W2067496326","https://openalex.org/W2070382733","https://openalex.org/W2080601382","https://openalex.org/W2098148222","https://openalex.org/W2105068790","https://openalex.org/W2110343796","https://openalex.org/W2112341373","https://openalex.org/W2134383774","https://openalex.org/W2135046866","https://openalex.org/W2156383199","https://openalex.org/W2167884573","https://openalex.org/W2171791029","https://openalex.org/W2250299594","https://openalex.org/W2329494830","https://openalex.org/W2417858809","https://openalex.org/W2540674420","https://openalex.org/W2582743722","https://openalex.org/W2608898041","https://openalex.org/W2752277700","https://openalex.org/W2895029330","https://openalex.org/W3020866103","https://openalex.org/W3106000725","https://openalex.org/W3123096029","https://openalex.org/W3123760665","https://openalex.org/W3124280487","https://openalex.org/W3124751173","https://openalex.org/W3124980728","https://openalex.org/W4226331836","https://openalex.org/W4229539396","https://openalex.org/W4230410911","https://openalex.org/W4291162556","https://openalex.org/W4386889777"],"related_works":["https://openalex.org/W2391958761","https://openalex.org/W2765453142","https://openalex.org/W2356780078","https://openalex.org/W2356008845","https://openalex.org/W255134961","https://openalex.org/W2348314720","https://openalex.org/W2243547089","https://openalex.org/W2316482937","https://openalex.org/W3089110333","https://openalex.org/W3134489511"],"abstract_inverted_index":{"Abstract":[0],"Many":[1],"modern":[2],"statistical":[3],"models":[4,17,90],"are":[5,18],"used":[6,19],"for":[7,20],"both":[8],"insight":[9],"and":[10,49,115,160,176],"prediction":[11,21,28],"when":[12],"applied":[13],"to":[14,44,46,101,111,121,186,205],"data.":[15],"When":[16],"one":[22],"should":[23],"optimise":[24],"parameters":[25],"through":[26],"a":[27,56,84,96,148,202],"error":[29],"loss":[30],"function.":[31],"Estimation":[32],"methods":[33],"based":[34],"on":[35,170],"multiple":[36,132],"steps":[37,133],"ahead":[38],"forecast":[39,161],"errors":[40],"have":[41],"been":[42],"shown":[43],"lead":[45],"more":[47],"robust":[48],"less":[50],"biased":[51],"estimates":[52],"of":[53,59,79,98,129,178],"parameters.":[54],"However,":[55,92],"plausible":[57],"explanation":[58],"why":[60],"this":[61,68,72,93],"is":[62,65,82,189,201],"the":[63,76,107,112,127,130,137,153,174,179,183,195,199],"case":[64],"lacking.":[66],"In":[67],"paper,":[69],"we":[70,135,164,192],"provide":[71],"explanation,":[73],"showing":[74,151],"that":[75,182,194],"main":[77],"benefit":[78],"these":[80],"estimators":[81,114,154],"in":[83,88],"shrinkage":[85,196],"effect,":[86],"happening":[87],"univariate":[89],"naturally.":[91],"can":[94],"introduce":[95],"series":[97,123],"limitations,":[99],"due":[100],"overly":[102],"aggressive":[103],"shrinkage.":[104],"We":[105,146],"discuss":[106],"predictive":[108],"likelihoods":[109],"related":[110],"multistep":[113],"demonstrate":[116],"what":[117],"their":[118],"usage":[119],"implies":[120],"time":[122],"models.":[124],"To":[125],"overcome":[126],"limitations":[128],"existing":[131],"estimators,":[134],"propose":[136],"Geometric":[138],"Trace":[139],"Mean":[140],"Squared":[141],"Error,":[142],"demonstrating":[143,173],"its":[144],"advantages.":[145],"conduct":[147],"simulation":[149],"experiment":[150],"how":[152],"behave":[155],"with":[156],"different":[157],"sample":[158],"sizes":[159],"horizons.":[162],"Finally,":[163],"carry":[165],"out":[166],"an":[167],"empirical":[168],"evaluation":[169],"real":[171],"data,":[172],"performance":[175],"advantages":[177],"estimators.":[180],"Given":[181],"underlying":[184],"process":[185],"be":[187],"modelled":[188],"often":[190],"unknown,":[191],"conclude":[193],"achieved":[197],"by":[198],"GTMSE":[200],"competitive":[203],"alternative":[204],"conventional":[206],"ones.":[207]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":3},{"year":2023,"cited_by_count":1}],"updated_date":"2026-08-18T07:49:30.821534","created_date":"2025-10-10T00:00:00"}
