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Under this framework, the limiting null distributions of the conventional unit root test statistics are derived and shown to contain a number of unknown parameters. To circumvent the difficulty of direct consistent estimation, we propose to use the dependent wild bootstrap to approximate the nonpivotal limiting null distributions and provide a rigorous theoretical justification for bootstrap consistency. The proposed method is compared through finite sample simulations with the recolored wild bootstrap procedure, which was developed for errors that follow a heteroscedastic linear process. Furthermore, a combination of autoregressive sieve recoloring with the dependent wild bootstrap is shown to perform well. The validity of the dependent wild bootstrap in a nonstationary setting is demonstrated for the first time, showing the possibility of extensions to other inference problems associated with locally stationary processes.<\/jats:p>","DOI":"10.1017\/s0266466618000038","type":"journal-article","created":{"date-parts":[[2018,4,12]],"date-time":"2018-04-12T09:50:21Z","timestamp":1523526621000},"page":"142-166","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":11,"title":["BOOTSTRAP-ASSISTED UNIT ROOT TESTING WITH PIECEWISE LOCALLY STATIONARY ERRORS"],"prefix":"10.1017","volume":"35","author":[{"given":"Yeonwoo","family":"Rho","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaofeng","family":"Shao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2018,4,12]]},"reference":[{"key":"S0266466618000038_ref11","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9892.00312"},{"key":"S0266466618000038_ref58","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2013.787184"},{"key":"S0266466618000038_ref8","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9892.2007.00557.x"},{"key":"S0266466618000038_ref5","doi-asserted-by":"publisher","DOI":"10.1198\/073500103288619269"},{"key":"S0266466618000038_ref18","doi-asserted-by":"publisher","DOI":"10.2307\/2171846"},{"key":"S0266466618000038_ref3","doi-asserted-by":"publisher","DOI":"10.2307\/2938229"},{"key":"S0266466618000038_ref13","doi-asserted-by":"publisher","DOI":"10.1214\/009053606000000227"},{"key":"S0266466618000038_ref15","doi-asserted-by":"publisher","DOI":"10.2307\/1912517"},{"key":"S0266466618000038_ref47","doi-asserted-by":"publisher","DOI":"10.1198\/jasa.2009.tm08744"},{"key":"S0266466618000038_ref4","volume-title":"Convergence of Probability Measures","author":"Billingsley","year":"1968"},{"key":"S0266466618000038_ref9","doi-asserted-by":"publisher","DOI":"10.1080\/07474930802467167"},{"key":"S0266466618000038_ref1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1998.10473808"},{"key":"S0266466618000038_ref12","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1214\/aos\/1034276620","article-title":"Fitting time series models to nonstationary processes","volume":"25","author":"Dahlhaus","year":"1997","journal-title":"The Annals of Statistics"},{"key":"S0266466618000038_ref16","unstructured":"Dom\u00ednguez M.A. & Lobato I.N. 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