{"id":"https://openalex.org/W2233802987","doi":"https://doi.org/10.1007/978-3-642-51514-9_4","title":"Testing for Causation Between Two Variables in Higher-Dimensional VAR Models","display_name":"Testing for Causation Between Two Variables in Higher-Dimensional VAR Models","publication_year":1993,"publication_date":"1993-01-01","ids":{"openalex":"https://openalex.org/W2233802987","doi":"https://doi.org/10.1007/978-3-642-51514-9_4","mag":"2233802987"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-642-51514-9_4","doi":"https://doi.org/10.1007/978-3-642-51514-9_4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-51514-9_4","pdf_url":null,"source":{"id":"https://openalex.org/S4210193918","display_name":"Contributions to economics","issn_l":"1431-1933","issn":["1431-1933","2197-7178"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","norway-1"],"host_organization":"https://openalex.org/P4310319972","host_organization_name":"Springer International Publishing","host_organization_lineage":["https://openalex.org/P4310319972","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer International Publishing","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Contributions to Economics","raw_type":"book-chapter"},"volume":{"id":"https://openalex.org/W646166725","display_name":"Studies in Applied Econometrics"},"type":"book-chapter","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/A5065670291","display_name":"Helmut L\u00fctkepohl","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I39343248","display_name":"Humboldt-Universit\u00e4t zu Berlin","ror":"https://ror.org/01hcx6992","country_code":"DE","type":"education","lineage":["https://openalex.org/I39343248"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Helmut L\u00fctkepohl","raw_affiliation_strings":["Humboldt University, Berlin, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Humboldt University, Berlin, Germany","institution_ids":["https://openalex.org/I39343248"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5065670291"],"corresponding_institution_ids":["https://openalex.org/I39343248"],"apc_list":null,"apc_paid":null,"fwci":9.5753,"has_fulltext":false,"cited_by_count":119,"citation_normalized_percentile":{"value":0.98066595,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"75","last_page":"91"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10007","display_name":"Monetary Policy and Economic Impact","score":0.5473999977111816,"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"}},"topics":[{"id":"https://openalex.org/T10007","display_name":"Monetary Policy and Economic Impact","score":0.5473999977111816,"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"}},{"id":"https://openalex.org/T13370","display_name":"Diverse Scientific and Economic Studies","score":0.08190000057220459,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.07779999822378159,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/granger-causality","display_name":"Granger causality","score":0.9279999732971191},{"id":"https://openalex.org/keywords/causality-tests","display_name":"causality testing","score":0.8339999914169312},{"id":"https://openalex.org/keywords/multivariate-time-series","display_name":"multivariate time series","score":0.656000018119812}],"concepts":[{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.6661117076873779},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6136298179626465},{"id":"https://openalex.org/C159877910","wikidata":"https://www.wikidata.org/wiki/Q2202883","display_name":"Autoregressive model","level":2,"score":0.4959135949611664},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4909375011920929},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.24680647253990173},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.15424421429634094},{"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:10.1007/978-3-642-51514-9_4","doi":"https://doi.org/10.1007/978-3-642-51514-9_4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-51514-9_4","pdf_url":null,"source":{"id":"https://openalex.org/S4210193918","display_name":"Contributions to economics","issn_l":"1431-1933","issn":["1431-1933","2197-7178"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","norway-1"],"host_organization":"https://openalex.org/P4310319972","host_organization_name":"Springer International Publishing","host_organization_lineage":["https://openalex.org/P4310319972","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer International Publishing","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Contributions to Economics","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1500470240","https://openalex.org/W1556920752","https://openalex.org/W1980362447","https://openalex.org/W1981248270","https://openalex.org/W1985822778","https://openalex.org/W2009245939","https://openalex.org/W2019459021","https://openalex.org/W2021586998","https://openalex.org/W2026590277","https://openalex.org/W2036146461","https://openalex.org/W2041951664","https://openalex.org/W2046291910","https://openalex.org/W2049807282","https://openalex.org/W2072040544","https://openalex.org/W2076342030","https://openalex.org/W2087964979","https://openalex.org/W2142635246","https://openalex.org/W2146855196","https://openalex.org/W2178225550","https://openalex.org/W2321974456","https://openalex.org/W2324882335","https://openalex.org/W2327683694","https://openalex.org/W2797856925","https://openalex.org/W3015236987","https://openalex.org/W3121726104","https://openalex.org/W4210681051","https://openalex.org/W4230750266","https://openalex.org/W4301134136"],"related_works":["https://openalex.org/W1542392666","https://openalex.org/W2105029674","https://openalex.org/W2004067290","https://openalex.org/W1526232314","https://openalex.org/W3130941099","https://openalex.org/W2915538716","https://openalex.org/W1633796845","https://openalex.org/W2156080281","https://openalex.org/W2094155635","https://openalex.org/W2753226022"],"abstract_inverted_index":{"Different":[0],"concepts":[1],"of":[2,58,112],"causality":[3],"in":[4,12,35,63,118],"vector":[5],"autoregressive":[6],"(VAR)":[7],"models":[8],"have":[9],"been":[10],"proposed":[11],"the":[13,31,37,47,56,60,64,107,175],"literature.":[14],"For":[15],"instance,":[16],"Granger":[17],"(1969)":[18],"defines":[19],"a":[20,129],"variable":[21],"y":[22,28,42,69,78,121,124],"2":[23,70,125],"to":[24,74,193,214],"be":[25,72,75],"causal":[26],"for":[27,77],"1":[29,79,122],"if":[30,80],"former":[32],"is":[33,178,191],"helpful":[34],"predicting":[36],"latter.":[38],"Formally,":[39],"denoting":[40],"by":[41,128],"1,t":[43],"(h|\u03a9":[44],"t":[45,53,67,114,180],")":[46],"optimal":[48],"h-step":[49],"predictor":[50],"at":[51],"origin":[52],"based":[54],"on":[55],"set":[57,108,177],"all":[59,110],"relevant":[61],"information":[62,176],"universe":[65],"\u03a9":[66,113,179],",":[68,101],"may":[71],"defined":[73],"Granger-noncausal":[76],"(1.1)":[81,190],"$$":[82,100,134,173,195,205],"{y_{1,t}}\\left(":[83,88],"{h|{\\Omega":[84,89],"_t}}":[85],"\\right)":[86],"=":[87,98,143,145,181,198,201],"_t}\\backslash":[90],"\\left\\{":[91],"{{y_{2,s}}":[92],"\\le":[93],"t}":[94,188],"\\right\\}}":[95],"\\right),\\quad":[96],"h":[97],"1,2,...":[99],"where":[102],"\u03a9t":[103],"\\":[104],"A":[105],"denotes":[106],"containing":[109],"elements":[111],"that":[115],"are":[116,126,212],"not":[117],"A.":[119],"If":[120],"and":[123,174],"generated":[127],"bivariate":[130],"VAR(p)":[131],"process":[132],"(1.2)":[133],"\\left[":[135],"\\begin{array}{l}":[136,148,160],"{y_{1t}}":[137],"\\\\":[138,140,153,164,168],"{y_{2t}}":[139],"\\end{array}":[141,169],"\\right]":[142,170],"\\sum\\limits_{i":[144],"1}^p":[146],"{\\left[":[147],"{\\alpha":[149,151,154,156,196],"_{11,i}}\\quad":[150],"_{12,i}}":[152,197],"_{21,i}}\\quad":[155],"_{22,i}}":[157],"\\\\\\end{array}":[158],"\\right]\\left[":[159],"{y_{1,t":[161],"-":[162,166],"i}}":[163,167],"{y_{2,t":[165],"+":[171],"{u_t}}":[172],"{(y":[182],"1,s":[183],",y":[184],"2,s":[185],")\u2032|s":[186],"\u2264":[187],"then":[189],"equivalent":[192],"(1.3)":[194],"0,\\quad":[199],"i":[200],"1,2,":[202],"\\ldots":[203],",p":[204],".":[206],"Under":[207],"standard":[208],"assumptions,":[209],"these":[210],"restrictions":[211],"easy":[213],"test.":[215]},"counts_by_year":[{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":9},{"year":2018,"cited_by_count":10},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":6}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2016-06-24T00:00:00"}
