{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,14]],"date-time":"2026-07-14T15:06:18Z","timestamp":1784041578737,"version":"3.55.0"},"reference-count":44,"publisher":"Informa UK Limited","license":[{"start":{"date-parts":[[2026,7,14]],"date-time":"2026-07-14T00:00:00Z","timestamp":1783987200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2026,7,14]],"date-time":"2026-07-14T00:00:00Z","timestamp":1783987200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/doi.org\/10.1080\/policies-text-data-mining"}],"content-domain":{"domain":["www.tandfonline.com"],"crossmark-restriction":true},"short-container-title":["Journal of the American Statistical Association"],"DOI":"10.1080\/01621459.2026.2695450","type":"journal-article","created":{"date-parts":[[2026,7,14]],"date-time":"2026-07-14T14:35:59Z","timestamp":1784039759000},"page":"1-27","update-policy":"https:\/\/doi.org\/10.1080\/tandf_crossmark_01","source":"Crossref","is-referenced-by-count":0,"title":["Canonical correlation analysis of stochastic trends via functional approximation"],"prefix":"10.1080","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3745-2233","authenticated-orcid":false,"given":"M.","family":"Franchi","sequence":"first","affiliation":[{"name":"Sapienza University of Rome","place":["Rome, Italy"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3392-806X","authenticated-orcid":false,"given":"I.","family":"Georgiev","sequence":"additional","affiliation":[{"name":"University of Bologna","place":["Bologna, Italy"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3982-4889","authenticated-orcid":false,"given":"P.","family":"Paruolo","sequence":"additional","affiliation":[{"name":"European Commission, Joint Research Centre (JRC)","place":["Ispra, Italy"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"301","published-online":{"date-parts":[[2026,7,14]]},"reference":[{"key":"e_1_3_1_2_1","doi-asserted-by":"crossref","unstructured":"Ahn S. and A. Horenstein (2013). Eigenvalue Ratio Test for the Number of Factors. Econometrica 81 1203\u20131227.","DOI":"10.3982\/ECTA8968"},{"key":"e_1_3_1_3_1","doi-asserted-by":"crossref","unstructured":"Ahn S. and C. Reinsel (1990). Estimation for partially nonstationary multivariate autoregressive models. Journal of the American Statistical Association 85 813\u201323.","DOI":"10.1080\/01621459.1990.10474945"},{"key":"e_1_3_1_4_1","doi-asserted-by":"publisher","DOI":"10.2307\/2938229"},{"key":"e_1_3_1_5_1","doi-asserted-by":"crossref","unstructured":"Andrews D. W. K. and J. C. Monahan (1992). An improved heteroskedasticity and autocorrelation consistent covariance matrix estimator. Econometrica 60(4) 953\u2013966.","DOI":"10.2307\/2951574"},{"key":"e_1_3_1_6_1","doi-asserted-by":"crossref","unstructured":"Bai J. (2004). Estimating cross-section common stochastic trends in nonstationary panel data. Journal of Econometrics 122 137\u2013183.","DOI":"10.1016\/j.jeconom.2003.10.022"},{"key":"e_1_3_1_7_1","doi-asserted-by":"crossref","unstructured":"Barigozzi M. G. Cavaliere and L. Trapani (2022). Inference in Heavy-Tailed Nonstationary Multivariate Time Series. Journal of the American Statistical Association 565\u2013581.","DOI":"10.1080\/01621459.2022.2128807"},{"key":"e_1_3_1_8_1","doi-asserted-by":"crossref","unstructured":"Bierens H. (1997). Nonparametric cointegration analysis. Journal of Econometrics 77 379\u2013404.","DOI":"10.1016\/S0304-4076(96)01820-9"},{"key":"e_1_3_1_9_1","doi-asserted-by":"crossref","unstructured":"Bykhovskaya A. and V. Gorin (2022). Cointegration in large VARs. The Annals of Statistics 50 1593 \u2013 1617.","DOI":"10.1214\/21-AOS2164"},{"key":"e_1_3_1_10_1","doi-asserted-by":"crossref","unstructured":"Bykhovskaya A. and V. Gorin (2024). Asymptotics of cointegration tests for high-dimensional VAR(k). The Review of Economics and Statistics 1\u201338.","DOI":"10.1162\/rest_a_01464"},{"key":"e_1_3_1_11_1","doi-asserted-by":"crossref","unstructured":"Cavaliere G. H. B. Nielsen and A. Rahbek (2015). Bootstrap testing of hypotheses on co-integration relations in vector autoregressive models. Econometrica 83 813\u2013831.","DOI":"10.3982\/ECTA11952"},{"key":"e_1_3_1_12_1","doi-asserted-by":"crossref","unstructured":"Cavaliere G. A. Rahbek and R. Taylor (2012). Bootstrap determination of the co-integration rank in vector autoregressive models. Econometrica 80 1721\u20131740.","DOI":"10.3982\/ECTA9099"},{"key":"e_1_3_1_13_1","doi-asserted-by":"crossref","unstructured":"Chen S. and M. Schienle (2024). Large Spillover Networks of Nonstationary Systems. Journal of Business & Economic Statistics 42 422\u2013436.","DOI":"10.1080\/07350015.2022.2099870"},{"key":"e_1_3_1_14_1","doi-asserted-by":"crossref","unstructured":"Elliott G. (1999). Efficient Tests for a Unit Root When the Initial Observation is Drawn from Its Unconditional Distribution. International Economic Review 40 767\u2013783.","DOI":"10.1111\/1468-2354.00039"},{"key":"e_1_3_1_15_1","doi-asserted-by":"crossref","unstructured":"Engle R. and C. Granger (1987). Co-integration and Error Correction: Representation Estimation and Testing. Econometrica 55 251\u2013276.","DOI":"10.2307\/1913236"},{"key":"e_1_3_1_16_1","unstructured":"Franchi M. I. Georgiev and P. Paruolo (2023). Estimating the number of common trends in large T and N factor models via canonical correlation analysis. Econometrics and Statistics forthcoming."},{"key":"e_1_3_1_17_1","doi-asserted-by":"crossref","unstructured":"Haug A. A. (2002). Testing linear restrictions on cointegrating vectors: sizes and powers of Wald and likelihood ratio tests in finite samples. Econometric Theory 18(2) 505\u2013524.","DOI":"10.1017\/S0266466602182119"},{"key":"e_1_3_1_18_1","doi-asserted-by":"crossref","unstructured":"Hwang J. and Y. Sun (2018). Simple robust and accurate F and t tests in cointegrated systems. Econometric Theory 34(5) 949\u2013984.","DOI":"10.1017\/S026646661700038X"},{"key":"e_1_3_1_19_1","doi-asserted-by":"crossref","unstructured":"Jacod J. and A. Shiryaev (2003). Limit Theorems for Stochastic Processes. Springer.","DOI":"10.1007\/978-3-662-05265-5"},{"key":"e_1_3_1_20_1","doi-asserted-by":"crossref","unstructured":"Johansen S. (1988). Statistical Analysis of Cointegration Vectors. Journal of Economic Dynamics and Control 12 231\u2013254.","DOI":"10.1016\/0165-1889(88)90041-3"},{"key":"e_1_3_1_21_1","doi-asserted-by":"crossref","unstructured":"Johansen S. (1991). Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models. Econometrica 59 1551\u20131580.","DOI":"10.2307\/2938278"},{"key":"e_1_3_1_22_1","doi-asserted-by":"crossref","unstructured":"Johansen S. (1996). Likelihood-based Inference in Cointegrated Vector Auto-Regressive Models. Oxford University Press.","DOI":"10.1093\/0198774508.001.0001"},{"key":"e_1_3_1_23_1","doi-asserted-by":"crossref","unstructured":"Johansen S. (2000). A Bartlett Correction Factor for Tests on the Cointegrating Relations. Econometric Theory 16 740\u2013778.","DOI":"10.1017\/S0266466600165065"},{"key":"e_1_3_1_24_1","doi-asserted-by":"crossref","unstructured":"Johansen S. (2002a). A small sample correction for tests of hypotheses on the cointegrating vectors. Journal of Econometrics 111 195\u2013221.","DOI":"10.1016\/S0304-4076(02)00104-5"},{"key":"e_1_3_1_25_1","doi-asserted-by":"crossref","unstructured":"Johansen S. (2002b). A Small Sample Correction for the Test of Cointegrating Rank in the Vector Autoregressive Model. Econometrica 70 1929\u20131961.","DOI":"10.1111\/1468-0262.00358"},{"key":"e_1_3_1_26_1","doi-asserted-by":"crossref","unstructured":"Liang C. and M. Schienle (2019). Determination of vector error correction models in high dimensions. Journal of Econometrics 208 418\u2013441.","DOI":"10.1016\/j.jeconom.2018.09.018"},{"key":"e_1_3_1_27_1","doi-asserted-by":"crossref","unstructured":"Lo\u00e8ve M. (1978). Probability theory II (4th ed.). Graduate Texts in Mathematics. Springer.","DOI":"10.1007\/978-1-4612-6257-2"},{"key":"e_1_3_1_28_1","doi-asserted-by":"crossref","unstructured":"M\u00fcller U. and M. Watson (2008). Testing Models of Low-Frequency Variability. Econometrica 76 979\u20131016.","DOI":"10.3982\/ECTA6814"},{"key":"e_1_3_1_29_1","doi-asserted-by":"crossref","unstructured":"M\u00fcller U. and M. Watson (2017). Low-Frequency Econometrics. In e.-a. Honor\u00e9 B. (Ed.) Advances in Economics and Econometrics: 11-th WC pp. 53\u201394. CUP.","DOI":"10.1017\/9781108227223.003"},{"key":"e_1_3_1_30_1","doi-asserted-by":"crossref","unstructured":"M\u00fcller U. and M. Watson (2018). Long-Run Covariability. Econometrica 86 775\u2013804.","DOI":"10.3982\/ECTA15047"},{"key":"e_1_3_1_31_1","doi-asserted-by":"crossref","unstructured":"Nielsen M. W. Seo and D. Seong (2022). Inference on the dimension of the nonstationary subspace in functional time series. Econometric Theory 39 443\u2013480.","DOI":"10.1017\/S0266466622000111"},{"key":"e_1_3_1_32_1","doi-asserted-by":"crossref","unstructured":"Onatski A. and C. Wang (2018). Alternative Asymptotics for Cointegration Tests in Large VARs. Econometrica 86 1465\u20131478.","DOI":"10.3982\/ECTA14649"},{"key":"e_1_3_1_33_1","doi-asserted-by":"crossref","unstructured":"Onatski A. and C. Wang (2019). Extreme canonical correlations and high-dimensional cointegration analysis. Journal of Econometrics 212 307\u2013322.","DOI":"10.1016\/j.jeconom.2019.04.032"},{"key":"e_1_3_1_34_1","doi-asserted-by":"crossref","unstructured":"Paruolo P. (1997). Asymptotic Inference on the Moving Average Impact Matrix in Cointegrated I(1) Var Systems. Econometric Theory 13 79\u2013118.","DOI":"10.1017\/S026646660000565X"},{"key":"e_1_3_1_35_1","doi-asserted-by":"crossref","unstructured":"Petersen A. C. Zhang and P. Kokoszka (2022). Modeling probability density functions as data objects. Econometrics and Statistics 21 159\u2013178.","DOI":"10.1016\/j.ecosta.2021.04.004"},{"key":"e_1_3_1_36_1","doi-asserted-by":"crossref","unstructured":"Phillips P. and B. Hansen (1990). Statistical inference in Instrumental Variables regression with I(1) processes. Review of Economic Studies 57(1) 99\u2013125.","DOI":"10.2307\/2297545"},{"key":"e_1_3_1_37_1","doi-asserted-by":"crossref","unstructured":"Phillips P. C. B. (1998). New Tools for Understanding Spurious Regressions. Econometrica 66 1299\u20131326.","DOI":"10.2307\/2999618"},{"key":"e_1_3_1_38_1","doi-asserted-by":"crossref","unstructured":"Phillips P. C. B. (2005). HAC Estimation by Automated Regression. Econometric Theory 21 116\u2013142.","DOI":"10.1017\/S0266466605050085"},{"key":"e_1_3_1_39_1","doi-asserted-by":"crossref","unstructured":"Phillips P. C. B. (2014). Optimal estimation of cointegrated systems with irrelevant instruments. Journal of Econometrics 178 210\u2013224.","DOI":"10.1016\/j.jeconom.2013.08.022"},{"key":"e_1_3_1_40_1","doi-asserted-by":"crossref","unstructured":"Phillips P. C. B. and V. Solo (1992). Asymptotics for Linear Processes. The Annals of Statistics 20 971 \u2013 1001.","DOI":"10.1214\/aos\/1176348666"},{"key":"e_1_3_1_41_1","doi-asserted-by":"crossref","unstructured":"Stock J. and M. Watson (1988). Testing for common trends. Journal of the American Statistical Society 83 1097\u20131107.","DOI":"10.1080\/01621459.1988.10478707"},{"key":"e_1_3_1_42_1","doi-asserted-by":"crossref","unstructured":"Sun Y. (2011). Robust trend inference with series variance estimator and testing-optimal smoothing parameter. Journal of Econometrics 164(2) 345\u2013366.","DOI":"10.1016\/j.jeconom.2011.06.017"},{"key":"e_1_3_1_43_1","doi-asserted-by":"crossref","unstructured":"Swensen A. (2006). Bootstrap Algorithms for Testing and Determining the Cointegration Rank in VAR Models. Econometrica 74 1699\u20131714.","DOI":"10.1111\/j.1468-0262.2006.00723.x"},{"key":"e_1_3_1_44_1","doi-asserted-by":"crossref","unstructured":"Watson M. W. (1994). Chapter 47: Vector autoregressions and cointegration. In R. F. Engle and D. L. McFadden (Eds.) Handbook of Econometrics Volume 4 pp. 2843\u20132915. Elsevier.","DOI":"10.1016\/S1573-4412(05)80016-9"},{"key":"e_1_3_1_45_1","doi-asserted-by":"crossref","unstructured":"Zhang R. P. Robinson and Q. Yao (2019). Identifying cointegration by eigenanalysis. Journal of the American Statistical Association 114 916\u2013927.","DOI":"10.1080\/01621459.2018.1458620"}],"container-title":["Journal of the American Statistical Association"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.tandfonline.com\/doi\/pdf\/10.1080\/01621459.2026.2695450","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.tandfonline.com\/doi\/full-xml\/10.1080\/01621459.2026.2695450","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.tandfonline.com\/doi\/pdf\/10.1080\/01621459.2026.2695450","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,7,14]],"date-time":"2026-07-14T14:36:08Z","timestamp":1784039768000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.tandfonline.com\/doi\/full\/10.1080\/01621459.2026.2695450"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,7,14]]},"references-count":44,"alternative-id":["10.1080\/01621459.2026.2695450"],"URL":"https:\/\/doi.org\/10.1080\/01621459.2026.2695450","relation":{},"ISSN":["0162-1459","1537-274X"],"issn-type":[{"value":"0162-1459","type":"print"},{"value":"1537-274X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,7,14]]},"assertion":[{"value":"The publishing and review policy for this title is described in its Aims & Scope.","order":1,"name":"peerreview_statement","label":"Peer Review Statement"},{"value":"http:\/\/www.tandfonline.com\/action\/journalInformation?show=aimsScope&journalCode=uasa20","URL":"http:\/\/www.tandfonline.com\/action\/journalInformation?show=aimsScope&journalCode=uasa20","order":2,"name":"aims_and_scope_url","label":"Aim & Scope"},{"value":"2024-12-18","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-04-07","order":1,"name":"revised","label":"Revised","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-06-16","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-07-14","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}