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For more refined analysis, the paper proposes and analyzes a modification of the Johansen test. The new test for the absence of cointegration converges to the partial sum of the Airy1 point process. Supporting Monte Carlo simulations indicate that the same behavior persists universally in many situations beyond those considered in our theorems. The paper presents empirical implementations of the approach for the analysis of S&amp;P100 stocks and of cryptocurrencies. The latter example has a strong presence of multiple cointegrating relationships, while the results for the former are consistent with the null of no cointegration.<\/jats:p>","DOI":"10.1162\/rest_a_01464","type":"journal-article","created":{"date-parts":[[2024,6,18]],"date-time":"2024-06-18T15:48:55Z","timestamp":1718725735000},"page":"1319-1331","update-policy":"https:\/\/doi.org\/10.1162\/mitpressjournals.corrections.policy","source":"Crossref","is-referenced-by-count":4,"title":["Asymptotics of Cointegration Tests for High-Dimensional Var(k)"],"prefix":"10.1162","volume":"108","author":[{"given":"Anna","family":"Bykhovskaya","sequence":"first","affiliation":[{"name":"Duke University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Vadim","family":"Gorin","sequence":"additional","affiliation":[{"name":"University of California at 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