{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,23]],"date-time":"2026-10-23T21:21:55Z","timestamp":1792790515065,"version":"4.5.0"},"reference-count":18,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2003,6]]},"abstract":"<jats:p>A wavelet-based forecasting method for time series is introduced. It is based on a multiple resolution decomposition of the signal, using the redundant \"\u00e0 trous\" wavelet transform which has the advantage of being shift-invariant.<\/jats:p><jats:p>The result is a decomposition of the signal into a range of frequency scales. The prediction is based on a small number of coefficients on each of these scales. In its simplest form it is a linear prediction based on a wavelet transform of the signal. This method uses sparse modelling, but can be based on coefficients that are summaries or characteristics of large parts of the signal. The lower level of the decomposition can capture the long-range dependencies with only a few coefficients, while the higher levels capture the usual short-term dependencies.<\/jats:p><jats:p>We show the convergence of the method towards the optimal prediction in the autoregressive case. The method works well, as shown in simulation studies, and studies involving financial data.<\/jats:p>","DOI":"10.1142\/s0219691303000153","type":"journal-article","created":{"date-parts":[[2003,7,8]],"date-time":"2003-07-08T10:12:53Z","timestamp":1057659173000},"page":"217-232","source":"Crossref","is-referenced-by-count":66,"title":["Prediction Based on a Multiscale Decomposition"],"prefix":"10.1142","volume":"01","author":[{"given":"Olivier","family":"Renaud","sequence":"first","affiliation":[{"name":"Facult\u00e9 de Psychologie et Sciences de l'Education, Universit\u00e9 de Gen\u00e8ve, 40, Bd du Pont d'Arve, 1211 Gen\u00e8ve 4, Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jean-Luc","family":"Starck","sequence":"additional","affiliation":[{"name":"DAPNIA\/SEI-SAP, Service d'Astrophysique, CEA-Saclay, 91191 Gif sur Yvette, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fionn","family":"Murtagh","sequence":"additional","affiliation":[{"name":"School of Computer Science, Queen's University Belfast, Belfast BT7 1NN, Northern Ireland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2012,1,5]]},"reference":[{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-0320-4"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1016\/B978-0-12-174590-5.50029-0"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-1684(97)00007-8"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-2544-7_9"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-1684(00)00104-3"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1109\/18.761321"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970104"},{"key":"rf10","volume-title":"Wavelets: Time-Frequency Methods and Phase-Space","author":"Dutilleux P.","year":"1987"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1109\/82.661660"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1109\/78.668554"},{"key":"rf13","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1080\/10618600.1996.10474693","volume":"5","author":"McCoy E. 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