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In the case of finite activity jumps, we derive the asymptotic distribution of the maximum of all the local statistics unaffected by jumps, which makes it feasible to control the limiting probability of the global type I error and demonstrate the power of the test. We also present the theoretical results to illustrate the behaviors of the test statistics in the presence of infinite activity jumps. Simulation studies indicate the favorable performance of the proposed test in finite samples, and we also apply the test to the stock price data of Apple and Microsoft.<\/jats:p>","DOI":"10.1017\/s0266466626100425","type":"journal-article","created":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T11:18:42Z","timestamp":1775474322000},"page":"1-42","source":"Crossref","is-referenced-by-count":0,"title":["RANDOMIZED TESTING FOR JUMP DETECTION"],"prefix":"10.1017","author":[{"given":"Yucheng","family":"Sun","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/01r5sf951","id-type":"ROR","asserted-by":"publisher"}],"name":"Capital University of Economics and Business"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2026,4,6]]},"reference":[{"key":"S0266466626100425_r29","volume-title":"The asymptotic theory of extreme order 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