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To derive the asymptotic test size and power, we establish a functional invariance principle for semimartingales under a strong mixing condition. The power properties are analyzed under alternatives featuring deterministic trends in the volatility curve dynamics. Application to S&amp;P 500 futures data provides strong evidence of nonstationary variation in the volatility pattern, with implications for real\u2010time risk management and market activity measurement, including identification of spot volatility and the size of price jumps.<\/jats:p>","DOI":"10.3982\/qe2644","type":"journal-article","created":{"date-parts":[[2025,7,25]],"date-time":"2025-07-25T08:54:29Z","timestamp":1753433669000},"page":"1059-1091","source":"Crossref","is-referenced-by-count":5,"title":["Testing mean stationarity of intraday volatility curves"],"prefix":"10.3982","volume":"16","author":[{"given":"Torben G.","family":"Andersen","sequence":"first","affiliation":[{"name":"Kellogg School of Management, Northwestern University"},{"name":"NBER, Canadian Derivatives Institute"},{"name":"CoRE, Aarhus"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yingwen","family":"Tan","sequence":"additional","affiliation":[{"name":"School of Statistics and Data Science, 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