[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-181846-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-181846-en":131},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","cointegration-and-vecm-test-results-lag-analysis","Cointegration and VECM Test Results - Lag Analysis","","Reported econometric results for a multivariate system using cointegration testing and Vector Error Correction Model (VECM) framework. T-statistics evaluate lagged variables across DKRE, DOET, DERG, DFAA, DOES, DCHA, DFAB, and DGAA against critical values. Eigenvalue and likelihood-ratio outputs support determining cointegrating relationships by hypothesized numbers of cointegrating equations. Error-correction coefficients, adjusted R-squared, F-statistics, and forecast gap ratios are summarized, alongside Granger causality tests over multiple lags using F-statistics.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/research-report/","Research & Report",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/cointegration-and-vecm-test-results-lag-analysis/181846/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/cointegration-and-vecm-test-results-lag-analysis/181846.png","ImageObject",300,407,{"name":42,"@type":43},"Rizky","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-24","2026-09-02",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",13,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What do the cointegration and eigenvalue tables indicate?","Question",{"text":63,"@type":64},"They report eigenvalues and likelihood-ratio statistics used to assess the number of cointegrating equations. Critical values support whether the hypothesized cointegration rank is retained or rejected.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How are error-correction terms interpreted in the VECM output?",{"text":68,"@type":64},"The error-correction section lists estimated coefficients for each differenced variable’s adjustment dynamics. Sign and magnitude (with t-statistics) show how strongly each equation responds to disequilibrium.",{"name":70,"@type":61,"acceptedAnswer":71},"What is tested in the Granger causality section?",{"text":72,"@type":64},"The tables test whether one variable helps predict another using lagged F-statistics under null hypotheses of “does not Granger cause.” Significant values indicate predictive causality at specific lags.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},181846,1788346197,{"code":4,"msg":82,"data":83},"success",[84,88,92,96,101,106,111,115,120,123,127],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":93,"show_sort_weight":94,"slug":95},"Exam",70,"exam",{"id":97,"doc_module":4,"doc_module_name":25,"category_name":98,"show_sort_weight":99,"slug":100},5,"Comic",60,"comic",{"id":102,"doc_module":4,"doc_module_name":25,"category_name":103,"show_sort_weight":104,"slug":105},6,"Technology",50,"technology",{"id":107,"doc_module":4,"doc_module_name":25,"category_name":108,"show_sort_weight":109,"slug":110},7,"Healthcare",40,"healthcare",{"id":112,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":113,"slug":114},8,30,"research-report",{"id":116,"doc_module":4,"doc_module_name":25,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":25,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":124,"doc_module":4,"doc_module_name":25,"category_name":125,"show_sort_weight":124,"slug":126},10,"Lifestyle","lifestyle",{"id":128,"doc_module":4,"doc_module_name":25,"category_name":129,"show_sort_weight":97,"slug":130},19,"General","general",{"code":4,"msg":82,"data":132},{"doc_id":79,"user_id":133,"nickname":42,"user_avatar":134,"doc_module":4,"category_id":112,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":124,"language":140,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":12,"update_tm":80,"read_time":144,"preview_page_count":4},962085564807,"https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","|  | T-statistics |  | Critical Value |  |  |\n| --- | --- | --- | --- | --- | --- |\n|  | lag=0 | lag=1 | 1% | 5% | 10% |\n| DKRE | -10.4084*** | -8.7719*** | -3.4734 | -2.8803 | -2.57687 |\n| DOET | -6.4242*** | -6.3160*** | -3.4734 | -2.8803 | -2.5769 |\n| DERG | -8.2367*** | -8.7174*** | -3.4734 | -2.8803 | -2.5769 |\n| DFAA | -8.8977*** | -8.2898*** | -3.4734 | -2.8803 | -2.5769 |\n| DOES | -10.0845*** | -8.2188*** | -3.4734 | -2.8803 | -2.5769 |\n| DCHA | -9.7184*** | -7.0530*** | -3.4731 | -2.8802 | -2.5768 |\n| DFAB | -8.9398*** | -10.3098*** | -3.4734 | -2.8803 | -2.5769 |\n| DGAA | -12.0461*** | -8.2053*** | -3.4734 | -2.8803 | -2.5769 |\n\n\n| r | Eigenvalue | Likelihood\u003Cbr>Ratio | 5% Critical\u003Cbr>Value | 1% Critical\u003Cbr>Value | Hypothesized No. of CEs |\n| --- | --- | --- | --- | --- | --- |\n| 0 | 0.3025 | 83.7291 | 53.12 | 60.16 | None** |\n| 1 | 0.1252 | 27.5212 | 34.91 | 41.07 | At most 1 |\n| 2 | 0.0218 | 6.6394 | 19.96 | 24.60 | At most 2 |\n\n\n| Cointegrating Equations |  |  |  |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| Variable | KRE(-1) | OET(-1) |  | ERG(-1) |  | FAA(-1) |  | C |  |\n|  | 1 | 76.932 | (8.298) | 0.152 | (3.073) | -0.030 | (-3.017) | -216.721 |  |\n| Error Correction : |  | D(KRE) |  | D(OET) |  | D(ERG) |  | D(FAA) |  |\n| CointeEq1 |  | -0.013 | (-0.992) | -0.002 | (-6.801) | -0.095 | (-1.484) | 0.167 | (1.100) |\n| D(KRE(-1)) |  | 0.058 | (0.653) | 0.003 | (1.663) | -0.119 | (-0.283) | 2.164 | (2.171) |\n| D(OET(-1)) |  | 6.282 | (2.328) | 0.527 | (8.366) | 3.656 | (0.289) | 31.257 | (1.044) |\n| D(ERG(-1)) |  | -0.045 | (-2.298) | -0.001 | (-3.190) | 0.285 | (3.083) | 0.366 | (1.673) |\n| D(FAA(-1)) |  | -0.020 | (-2.526) | 0.000 | (1.943) | -0.051 | (-1.349) | 0.216 | (2.409) |\n| C |  | 0.226 | (0.462) | -0.005 | (-0.455) | -0.570 | (-0.248) | 6.470 | (1.189) |\n| Adj. R-squared |  | 0.073 |  | 0.513 |  | 0.137 |  | 0.088 |  |\n| F-statistic |  | 3.412 |  | 33.111 |  | 5.857 |  | 3.939 |  |\n| Log Likelihood |  | -488.687 |  | 86.008 |  | -724.794 |  | -856.884 |  |\n\n| Section |  | Dec. 2014 | Jan. 2015 | Feb. 2015 | PRMSE |\n| --- | --- | --- | --- | --- | --- |\n| Actual value |  | -0.0551 | -0.0026 | 0.0255 |  |\n| VECM | Predicted value | 0.0072 | 0.0149 | 0.0002 | 3.9818 |\n|  | Gap ratio | -1.1306 | -6.7307 | 0.9921 |  |\n\n\n| Null hypothesis |  |  | F-statistic |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  |  |  | lag1 | lag2 | lag3 | lag4 | lag6 | lag8 | lag12 |\n| SKRE Granger SOET | does | not Cause | 3.509** | 1.797 | 2.650** | 2.158* | 1.758 | 3.328*** | 3.064*** |\n| SOET Granger SKRE | does | not Cause | 5.428** | 4.483** | 3.282** | 2.742** | 1.792 | 1.333 | 1.576* |\n| SKRE Granger SERG | does | not Cause | 0.346 | 0.622 | 0.743 | 4.872*** | 5.167*** | 4.015** | 2.656** |\n| SERG Granger SKRE | does | not Cause | 2.625* | 1.715 | 1.147 | 1.420 | 1.765* | 1.122 | 1.087 |\n| SKRE Granger SFAA | does | not Cause | 3.408** | 1.933 | 1.214 | 3.666*** | 2.867*** | 1.998** | 1.931** |\n| SFAA Granger SKRE | does | not Cause | 0.183 | 0.679 | 2.303* | 1.524 | 1.181 | 1.039 | 1.818* |\n| SKRE Granger SOES | does | not Cause | 3.476* | 2.299* | 1.686 | 1.271 | 1.137 | 1.139 | 0.850 |\n| SOES Granger SKRE | does | not Cause | 1.355 | 1.367 | 0.946 | 0.821 | 0.719 | 0.956 | 0.884 |\n| SKRE Granger SCHA | does | not Cause | 0.454 | 0.955 | 0.734 | 0.675 | 0.574 | 0.695 | 0.729 |\n| SCHA Granger SKRE | does | not Cause | 1.233 | 0.847 | 0.983 | 1.163 | 1.286 | 1.009 | 1.087 |\n| SKRE Granger SFAB | does | not Cause | 0.033 | 0.057 | 0.237 | 0.211 | 0.445 | 0.349 | 0.949 |\n| SFAB Granger SKRE | does | not Cause | 0.014 | 0.565 | 6.549*** | 5.776** | 4.011** | 3.388** | 2.344* |\n\n\n| SKRE does not Granger Cause GAA | 2.229 | 1.093 | 1.450 | 1.708 | 1.809 | 2.181 | 1.523 |\n| --- | --- | --- | --- | --- | --- | --- | --- |\n| SGAA does not\u003Cbr>Granger Cause\u003Cbr>SKRE | 0.055 | 1.298 | 0.869 | 0.614 | 0.509 | 0.309 | 0.313 |\n\n\n|  | Lag |  |  |  |  |  |  |\n| --- ","cbCaifgsT1B9iMMJ","https://ap.wps.com/l/cbCaifgsT1B9iMMJ","pdf",312160,"English","# Cointegration Test Results\n## T-statistics by Lag\n## Eigenvalues and Likelihood Ratio\n## Cointegrating Equations and Error Correction\n## Forecast Comparison via VECM\n## Granger Causality Tests","[{\"question\":\"What do the cointegration and eigenvalue tables indicate?\",\"answer\":\"They report eigenvalues and likelihood-ratio statistics used to assess the number of cointegrating equations. Critical values support whether the hypothesized cointegration rank is retained or rejected.\"},{\"question\":\"How are error-correction terms interpreted in the VECM output?\",\"answer\":\"The error-correction section lists estimated coefficients for each differenced variable’s adjustment dynamics. Sign and magnitude (with t-statistics) show how strongly each equation responds to disequilibrium.\"},{\"question\":\"What is tested in the Granger causality section?\",\"answer\":\"The tables test whether one variable helps predict another using lagged F-statistics under null hypotheses of “does not Granger cause.” Significant values indicate predictive causality at specific lags.\"}]","Cointegration and VECM Test Results - Lag Analysis | PDF",25]