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The paper introduces a new test for second-order stationarity that detects kinds of departures from stationarity that are different from those based on Fourier methods. The new test is also computationally fast, designed to work with Gaussian and a wide range of non-Gaussian time series, and can locate non-stationarities in time and scale. The test is demonstrated on earthquake, explosion, infant electrocardiogram and simulated time series showing varying degrees of stationarity. The second main contribution develops approximate confidence intervals for time varying autocovariances for locally stationary series as the usual bands computed for stationary series are not appropriate. Our new bands enable practitioners to assess time varying autocovariances statistically and are exhibited on localized autocovariances of explosion and simulated time series.<\/jats:p>","DOI":"10.1111\/rssb.12015","type":"journal-article","created":{"date-parts":[[2013,3,20]],"date-time":"2013-03-20T09:18:20Z","timestamp":1363771100000},"page":"879-904","source":"Crossref","is-referenced-by-count":85,"title":["A Test for Second-Order Stationarity and Approximate Confidence Intervals for Localized Autocovariances for Locally Stationary Time Series"],"prefix":"10.1093","volume":"75","author":[{"given":"Guy","family":"Nason","sequence":"first","affiliation":[{"name":"University of Bristol , UK"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2013,3,20]]},"reference":[{"key":"2023031306052484900_","doi-asserted-by":"crossref","first-page":"1488","DOI":"10.1080\/01621459.1998.10473808","article-title":"Time-dependent spectral analysis of nonstationary time series","volume":"93","author":"Adak","year":"1998","journal-title":"J. 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