{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T11:43:04Z","timestamp":1753875784665,"version":"3.41.2"},"reference-count":53,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2025,3,13]],"date-time":"2025-03-13T00:00:00Z","timestamp":1741824000000},"content-version":"vor","delay-in-days":71,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,3,16]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>This article introduces the class of continuous-time locally stationary wavelet processes. Continuous-time models enable us to properly provide scale-based time series models for irregularly spaced observations for the first time, while also permitting a spectral representation of the process over a continuous range of scales. We derive results for both the theoretical setting, where we assume access to the entire process sample path, and a more practical one, which develops methods for estimating the quantities of interest from sampled time series. The latter estimates are accurately computable in reasonable time by solving the relevant linear integral equation using the iterative soft-thresholding algorithm of Daubechies et\u00a0al. (2004). Appropriate smoothing techniques are also developed and applied in this new setting. Comparisons to previous methods are conducted on the heart rate time series of a sleeping infant. Additionally, we exemplify our new methods by computing spectral and autocovariance estimates on irregularly spaced heart rate data obtained from a recent sleep-state study.<\/jats:p>","DOI":"10.1093\/biomet\/asaf015","type":"journal-article","created":{"date-parts":[[2025,3,13]],"date-time":"2025-03-13T19:05:17Z","timestamp":1741892717000},"source":"Crossref","is-referenced-by-count":0,"title":["Continuous-time locally stationary wavelet processes"],"prefix":"10.1093","volume":"112","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2049-1161","authenticated-orcid":false,"given":"H A","family":"Palasciano","sequence":"first","affiliation":[{"name":"Department of Mathematics, Imperial College London , 180 Queen\u2019s Gate , South Kensington, London SW7 2AZ,","place":["UK"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M I","family":"Knight","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of York , Heslington, York YO10 5DD ,","place":["UK"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"G P","family":"Nason","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Imperial College London , 180 Queen\u2019s Gate , South Kensington, London SW7 2AZ,","place":["UK"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2025,3,13]]},"reference":[{"key":"2025062913170376700_asaf015-B1","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511809781","volume-title":"L\u00e9vy Processes and Stochastic Calculus","author":"Applebaum","year":"2009"},{"key":"2025062913170376700_asaf015-B2","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-319-94129-5","volume-title":"Ambit Stochastics","author":"Barndorff-Nielsen","year":"2018"},{"key":"2025062913170376700_asaf015-B3","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1137\/080716542","article-title":"A fast iterative shrinkage-thresholding algorithm for linear inverse problems","volume":"2","author":"Beck","year":"2009","journal-title":"SIAM J. 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