{"id":"https://openalex.org/W2905083307","doi":"https://doi.org/10.1111/j.2517-6161.1976.tb01585.x","title":"Forecasting Transformed Series","display_name":"Forecasting Transformed Series","publication_year":1976,"publication_date":"1976-01-01","ids":{"openalex":"https://openalex.org/W2905083307","doi":"https://doi.org/10.1111/j.2517-6161.1976.tb01585.x","mag":"2905083307"},"language":"en","primary_location":{"id":"doi:10.1111/j.2517-6161.1976.tb01585.x","doi":"https://doi.org/10.1111/j.2517-6161.1976.tb01585.x","is_oa":false,"landing_page_url":"https://doi.org/10.1111/j.2517-6161.1976.tb01585.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/A5105834520","display_name":"Clive W. J. Granger","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I142263535","display_name":"University of Nottingham","ror":"https://ror.org/01ee9ar58","country_code":"GB","type":"education","lineage":["https://openalex.org/I142263535"]},{"id":"https://openalex.org/I36258959","display_name":"University of California San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["GB","US"],"is_corresponding":false,"raw_author_name":"C. W. J. Granger","raw_affiliation_strings":["University of Nottingham and University of California , San Diego"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Nottingham and University of California , San Diego","institution_ids":["https://openalex.org/I142263535","https://openalex.org/I36258959"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108202560","display_name":"Paul Newbold","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I142263535","display_name":"University of Nottingham","ror":"https://ror.org/01ee9ar58","country_code":"GB","type":"education","lineage":["https://openalex.org/I142263535"]},{"id":"https://openalex.org/I36258959","display_name":"University of California San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["GB","US"],"is_corresponding":false,"raw_author_name":"P. Newbold","raw_affiliation_strings":["University of Nottingham and University of California , San Diego"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Nottingham and University of California , San Diego","institution_ids":["https://openalex.org/I142263535","https://openalex.org/I36258959"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2621,"currency":"GBP","value_usd":3456},"apc_paid":null,"fwci":18.3456,"has_fulltext":false,"cited_by_count":297,"citation_normalized_percentile":{"value":0.99562842,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"38","issue":"2","first_page":"189","last_page":"203"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11918","display_name":"Forecasting Techniques and Applications","score":0.6445000171661377,"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":0.6445000171661377,"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/T12205","display_name":"Time Series Analysis and Forecasting","score":0.2502000033855438,"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/T13487","display_name":"Statistical and numerical algorithms","score":0.061000000685453415,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/hermite-polynomial-expansion","display_name":"Hermite polynomial expansion","score":0.8640000224113464},{"id":"https://openalex.org/keywords/stationary-gaussian-processes","display_name":"stationary Gaussian processes","score":0.7889999747276306},{"id":"https://openalex.org/keywords/differencing","display_name":"differencing","score":0.5910000205039978},{"id":"https://openalex.org/keywords/time-series-forecasting","display_name":"time series forecasting","score":0.5519999861717224}],"concepts":[{"id":"https://openalex.org/C88271906","wikidata":"https://www.wikidata.org/wiki/Q786973","display_name":"Autocovariance","level":3,"score":0.8824215531349182},{"id":"https://openalex.org/C201362023","wikidata":"https://www.wikidata.org/wiki/Q658574","display_name":"Hermite polynomials","level":2,"score":0.8337020874023438},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.701384425163269},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.5685346722602844},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5650050640106201},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5291647911071777},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4624519646167755},{"id":"https://openalex.org/C110405555","wikidata":"https://www.wikidata.org/wiki/Q1192209","display_name":"Stationary process","level":2,"score":0.4501308798789978},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4245874285697937},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.42278599739074707},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.18514636158943176},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15946245193481445},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08644017577171326},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.055110663175582886},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1111/j.2517-6161.1976.tb01585.x","doi":"https://doi.org/10.1111/j.2517-6161.1976.tb01585.x","is_oa":false,"landing_page_url":"https://doi.org/10.1111/j.2517-6161.1976.tb01585.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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W27682692","https://openalex.org/W129305155","https://openalex.org/W1973014977","https://openalex.org/W1982051104","https://openalex.org/W1986528915","https://openalex.org/W2054510061","https://openalex.org/W2086453666","https://openalex.org/W2160465108","https://openalex.org/W2323285777","https://openalex.org/W2795391743","https://openalex.org/W2800702870","https://openalex.org/W4292483811"],"related_works":["https://openalex.org/W2019262607","https://openalex.org/W1994374441","https://openalex.org/W2039376519","https://openalex.org/W3004454395","https://openalex.org/W3113762380","https://openalex.org/W2069134978","https://openalex.org/W6925459452","https://openalex.org/W7161684544","https://openalex.org/W2152209375","https://openalex.org/W1976578188"],"abstract_inverted_index":{"Summary":[0],"Suppose":[1],"that":[2,13,26],"a":[3,68],"forecasting":[4,50],"model":[5],"is":[6,28],"available":[7],"for":[8,49,67],"the":[9,17,24,43,51,57],"process":[10],"Xt":[11,27],"but":[12],"interest":[14],"centres":[15],"on":[16],"instantaneous":[18,73],"transformation":[19],"Yt":[20],"=":[21],"T(Xt).":[22],"On":[23],"assumption":[25],"Gaussian":[29],"and":[30,47],"stationary,":[31],"or":[32],"can":[33],"be":[34,65],"reduced":[35],"to":[36,64],"stationarity":[37],"by":[38],"differencing,":[39],"this":[40],"paper":[41],"examines":[42],"autocovariance":[44],"structure":[45],"of":[46,72],"methods":[48],"transformed":[52],"series.":[53],"The":[54],"development":[55],"employs":[56],"Hermite":[58],"polynomial":[59],"expansion,":[60],"thus":[61],"allowing":[62],"results":[63],"derived":[66],"very":[69],"general":[70],"class":[71],"transformations.":[74]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":13},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":12},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":14}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2018-12-22T00:00:00"}