{"id":"https://openalex.org/W2121884826","doi":"https://doi.org/10.1109/tit.2009.2039158","title":"Long-Term Prediction Intervals of Time Series","display_name":"Long-Term Prediction Intervals of Time Series","publication_year":2010,"publication_date":"2010-03-01","ids":{"openalex":"https://openalex.org/W2121884826","doi":"https://doi.org/10.1109/tit.2009.2039158","mag":"2121884826"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2009.2039158","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2009.2039158","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"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 Information Theory","raw_type":"journal-article"},"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/A5100359926","display_name":"Zhou Zhou","orcid":"https://orcid.org/0000-0002-6490-8945"},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Zhou Zhou","raw_affiliation_strings":["Department of Statistics, University of Toronto, Toronto, ONT, Canada","Dept. of Stat., Univ. of Toronto, Toronto, ON, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics, University of Toronto, Toronto, ONT, Canada","institution_ids":["https://openalex.org/I185261750"]},{"raw_affiliation_string":"Dept. of Stat., Univ. of Toronto, Toronto, ON, Canada","institution_ids":["https://openalex.org/I185261750"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101816989","display_name":"Zhiwei Xu","orcid":"https://orcid.org/0000-0002-0401-8481"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]},{"id":"https://openalex.org/I4210130704","display_name":"University of Michigan\u2013Dearborn","ror":"https://ror.org/035wtm547","country_code":"US","type":"education","lineage":["https://openalex.org/I4210130704"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zhiwei Xu","raw_affiliation_strings":["Department of Computer and Information Science, University of Michigan, Dearborn, Dearborn, MI, USA","Department of Computer and Information Science, University of Michigan--Dearborn, Dearborn, MI, USA,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer and Information Science, University of Michigan, Dearborn, Dearborn, MI, USA","institution_ids":["https://openalex.org/I4210130704"]},{"raw_affiliation_string":"Department of Computer and Information Science, University of Michigan--Dearborn, Dearborn, MI, USA,","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036683934","display_name":"Wei Biao Wu","orcid":"https://orcid.org/0000-0003-4310-9965"},"institutions":[{"id":"https://openalex.org/I40347166","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28","country_code":"US","type":"education","lineage":["https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Wei Biao Wu","raw_affiliation_strings":["Department of Statistics, University of Chicago, Chicago, IL, USA","Dept. of Stat., Univ. of Chicago, Chicago, IL, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics, University of Chicago, Chicago, IL, USA","institution_ids":["https://openalex.org/I40347166"]},{"raw_affiliation_string":"Dept. of Stat., Univ. of Chicago, Chicago, IL, USA","institution_ids":["https://openalex.org/I40347166"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8536,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.77194021,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"56","issue":"3","first_page":"1436","last_page":"1446"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.9979000091552734,"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/T10136","display_name":"Statistical Methods and Inference","score":0.9979000091552734,"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/T10876","display_name":"Fault Detection and Control Systems","score":0.9952999949455261,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T11443","display_name":"Advanced Statistical Process Monitoring","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.8207368850708008},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.7092955112457275},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.6850532293319702},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.6563720107078552},{"id":"https://openalex.org/keywords/contrast","display_name":"Contrast (vision)","score":0.5556594133377075},{"id":"https://openalex.org/keywords/infinity","display_name":"Infinity","score":0.5352625846862793},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5036467909812927},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4651281535625458},{"id":"https://openalex.org/keywords/time-series","display_name":"Time series","score":0.46387872099876404},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.42884135246276855},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.41835087537765503},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.41642531752586365},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3870580196380615},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.29311174154281616},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.28600838780403137}],"concepts":[{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.8207368850708008},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.7092955112457275},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.6850532293319702},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.6563720107078552},{"id":"https://openalex.org/C2776502983","wikidata":"https://www.wikidata.org/wiki/Q690182","display_name":"Contrast (vision)","level":2,"score":0.5556594133377075},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.5352625846862793},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5036467909812927},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4651281535625458},{"id":"https://openalex.org/C151406439","wikidata":"https://www.wikidata.org/wiki/Q186588","display_name":"Time series","level":2,"score":0.46387872099876404},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.42884135246276855},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.41835087537765503},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41642531752586365},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3870580196380615},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.29311174154281616},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.28600838780403137},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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},{"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2009.2039158","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2009.2039158","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"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 Information Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320307817","display_name":"Time Warner","ror":"https://ror.org/045xx6g59"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":56,"referenced_works":["https://openalex.org/W49377464","https://openalex.org/W595580781","https://openalex.org/W629979766","https://openalex.org/W1490535108","https://openalex.org/W1513487224","https://openalex.org/W1523228994","https://openalex.org/W1546692449","https://openalex.org/W1609553728","https://openalex.org/W1982389390","https://openalex.org/W1997733220","https://openalex.org/W2009326110","https://openalex.org/W2013610892","https://openalex.org/W2021785397","https://openalex.org/W2028026621","https://openalex.org/W2038856402","https://openalex.org/W2053506130","https://openalex.org/W2065967197","https://openalex.org/W2068614941","https://openalex.org/W2069508080","https://openalex.org/W2073123379","https://openalex.org/W2083459869","https://openalex.org/W2089132889","https://openalex.org/W2093989891","https://openalex.org/W2096904991","https://openalex.org/W2104125428","https://openalex.org/W2105119576","https://openalex.org/W2120793724","https://openalex.org/W2129962685","https://openalex.org/W2130126601","https://openalex.org/W2133648300","https://openalex.org/W2143082178","https://openalex.org/W2158685529","https://openalex.org/W2160292396","https://openalex.org/W2164376107","https://openalex.org/W2165796148","https://openalex.org/W2316706700","https://openalex.org/W2489822048","https://openalex.org/W2502496670","https://openalex.org/W2751862591","https://openalex.org/W2798461040","https://openalex.org/W2798649148","https://openalex.org/W2798750840","https://openalex.org/W2964251103","https://openalex.org/W3015894552","https://openalex.org/W3100228156","https://openalex.org/W3101802582","https://openalex.org/W3105834982","https://openalex.org/W3124158937","https://openalex.org/W3146720720","https://openalex.org/W4233809357","https://openalex.org/W4238789398","https://openalex.org/W4242671632","https://openalex.org/W4248370127","https://openalex.org/W4292963524","https://openalex.org/W4299432846","https://openalex.org/W6653615545"],"related_works":["https://openalex.org/W2306553012","https://openalex.org/W4251417359","https://openalex.org/W4229993731","https://openalex.org/W2381059884","https://openalex.org/W2372756075","https://openalex.org/W1979193983","https://openalex.org/W2220405813","https://openalex.org/W1821795854","https://openalex.org/W2374111230","https://openalex.org/W2941119120"],"abstract_inverted_index":{"We":[0],"consider":[1],"the":[2,23,40,45,56,66,79],"problem":[3,26],"of":[4,9,12,39,47,58,65,81],"predicting":[5],"aggregates":[6,48],"or":[7],"sums":[8],"future":[10,34],"values":[11,38],"a":[13],"process":[14],"based":[15],"on":[16],"its":[17],"past":[18,37],"values.":[19],"In":[20],"contrast":[21],"with":[22,53],"conventional":[24],"prediction":[25,67,83],"in":[27,42],"which":[28],"one":[29],"predicts":[30],"<i":[31],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[32],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">a</i>":[33],"value":[35],"given":[36],"process,":[41],"our":[43],"setting":[44],"number":[46,57],"can":[49],"go":[50],"to":[51,55,77],"infinity":[52],"respect":[54],"available":[59],"observations.":[60],"Consistency":[61],"and":[62],"Bahadur":[63],"representations":[64],"estimators":[68],"are":[69],"established.":[70],"A":[71],"simulation":[72],"study":[73],"is":[74],"carried":[75],"out":[76],"assess":[78],"performance":[80],"different":[82],"estimators.":[84]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
