{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T10:35:17Z","timestamp":1790850917800,"version":"4.1.0"},"reference-count":0,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2000,7,1]],"date-time":"2000-07-01T00:00:00Z","timestamp":962409600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2000,7,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n               <jats:p>This paper defines and studies a new class of non-stationary random processes constructed from discrete non-decimated wavelets which generalizes the Cram\u00e9r (Fourier) representation of stationary time series. We define an evolutionary wavelet spectrum (EWS) which quantifies how process power varies locally over time and scale. We show how the EWS may be rigorously estimated by a smoothed wavelet periodogram and how both these quantities may be inverted to provide an estimable time-localized autocovariance. We illustrate our theory with a pedagogical example based on discrete non-decimated Haar wavelets and also a real medical time series example.<\/jats:p>","DOI":"10.1111\/1467-9868.00231","type":"journal-article","created":{"date-parts":[[2003,3,12]],"date-time":"2003-03-12T19:36:21Z","timestamp":1047497781000},"page":"271-292","source":"Crossref","is-referenced-by-count":250,"title":["Wavelet Processes and Adaptive Estimation of the Evolutionary Wavelet Spectrum"],"prefix":"10.1093","volume":"62","author":[{"given":"Guy P.","family":"Nason","sequence":"first","affiliation":[{"name":"University of Bristol , UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"R.","family":"Von Sachs","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Catholique de Louvain , Belgium"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gerald","family":"Kroisandt","sequence":"additional","affiliation":[{"name":"Universit\u00e4t Kaiserslautern , Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2002,1,6]]},"container-title":["Journal of the Royal Statistical Society Series B: Statistical Methodology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1111%2F1467-9868.00231","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/62\/2\/271\/49589721\/jrsssb_62_2_271.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/62\/2\/271\/49589721\/jrsssb_62_2_271.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,22]],"date-time":"2023-03-22T06:58:43Z","timestamp":1679468323000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/62\/2\/271\/7083237"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,7,1]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2002,1,6]]},"published-print":{"date-parts":[[2000,7,1]]}},"URL":"https:\/\/doi.org\/10.1111\/1467-9868.00231","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"value":"1369-7412","type":"print"},{"value":"1467-9868","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2000,7]]},"published":{"date-parts":[[2000,7,1]]}}}