{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:52:00Z","timestamp":1760143920484,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2024,3,1]],"date-time":"2024-03-01T00:00:00Z","timestamp":1709251200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We propose a two-sample testing procedure for high-dimensional time series. To obtain the asymptotic distribution of our \u2113\u221e-type test statistic under the null hypothesis, we establish high-dimensional central limit theorems (HCLTs) for an \u03b1-mixing sequence. Specifically, we derive two HCLTs for the maximum of a sum of high-dimensional \u03b1-mixing random vectors under the assumptions of bounded finite moments and exponential tails, respectively. The proposed HCLT for \u03b1-mixing sequence under bounded finite moments assumption is novel, and in comparison with existing results, we improve the convergence rate of the HCLT under the exponential tails assumption. To compute the critical value, we employ the blockwise bootstrap method. Importantly, our approach does not require the independence of the two samples, making it applicable for detecting change points in high-dimensional time series. Numerical results emphasize the effectiveness and advantages of our method.<\/jats:p>","DOI":"10.3390\/e26030226","type":"journal-article","created":{"date-parts":[[2024,3,1]],"date-time":"2024-03-01T11:19:24Z","timestamp":1709291964000},"page":"226","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Blockwise Bootstrap-Based Two-Sample Test for High-Dimensional Time Series"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-9291-6162","authenticated-orcid":false,"given":"Lin","family":"Yang","sequence":"first","affiliation":[{"name":"Joint Laboratory of Data Science and Business Intelligence, Southwestern University of Finance and Economics, Chengdu 611130, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,3,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"360","DOI":"10.1214\/aoms\/1177732979","article-title":"The generalization of student\u2019s ratio","volume":"2","author":"Hotelling","year":"1931","journal-title":"Ann. 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