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To accommodate the nonstationarity and other possible complex features, such as discontinuous trajectories, and heterogeneous partial measurement error of contemporary functional data, we propose methods that do not rest on the preprocessing techniques of presmoothing and dimension-reduction, which would be less accurate without the assumptions of stationarity and continuous trajectories. For detecting changes, we propose a bootstrap-assisted test for structural breaks among all mean trajectories, which is asymptotically correct and can detect local alternatives of n\u22121\/2. For localizing changes, we develop practical and consistent algorithms for estimating single and multiple change points, which further enable the estimation of mean trajectories. To establish the theoretical properties of our approaches, we develop a new backward martingale difference inequality and a functional Burkholder inequality for nonstationary functional time series, which can be of independent interest. The effectiveness of our approach is demonstrated through extensive simulation studies and real data analyses. The proposed algorithms in this article are available in the R package fcpseed.<\/jats:p>","DOI":"10.1093\/jrsssb\/qkag072","type":"journal-article","created":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T11:49:16Z","timestamp":1776858556000},"source":"Crossref","is-referenced-by-count":1,"title":["Inference for structural changes in nonstationary functional time series with partial measurement error"],"prefix":"10.1093","author":[{"given":"Lujia","family":"Bai","sequence":"first","affiliation":[{"name":"Fakult\u00e4t f\u00fcr Mathematik, Ruhr-Universit\u00e4t Bochum , 44780 Bochum ,","place":["Germany"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qirui","family":"Hu","sequence":"additional","affiliation":[{"name":"School of Statistics and Data Science, Shanghai University of Finance and Economics , 200433 Shanghai ,","place":["China"]},{"name":"Institute of Big Data Research, Shanghai University of Finance and Economics , 200433 Shanghai ,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Weichi","family":"Wu","sequence":"additional","affiliation":[{"name":"Department of Statistics and Data Science, Tsinghua University , 100084 Beijing ,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2026,5,19]]},"reference":[{"key":"2026051910423105900_qkag072-B1","doi-asserted-by":"publisher","first-page":"204","DOI":"10.1016\/j.jmva.2012.03.006","article-title":"Detecting and estimating changes in dependent functional data","volume":"109","author":"Aston","year":"2012","journal-title":"Journal of Multivariate Analysis"},{"issue":"10","key":"2026051910423105900_qkag072-B2","doi-asserted-by":"publisher","first-page":"2254","DOI":"10.1016\/j.jmva.2009.04.001","article-title":"Estimation of a change-point in the mean function of functional data","volume":"100","author":"Aue","year":"2009","journal-title":"Journal of Multivariate 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