{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T02:44:02Z","timestamp":1778553842957,"version":"3.51.4"},"reference-count":11,"publisher":"World Scientific Pub Co Pte Ltd","issue":"08","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2003,8]]},"abstract":"<jats:p>We generalize a method of noise estimation for chaotic time series due to [Schreiber, 1993] in cases where the noise level is relatively large. The noise estimation is based on the correlation integral, which, for small amounts of noise, is not affected by the attractor's curvature effects. When the noise is large, however, one has to increase the range of the correlation integral and this brings about significant inaccuracies in its evaluation due to both curvature effects and noise. In this Letter, we present a modification of Schreiber's noise level estimation method, which uses a robust error estimator based on L<jats:sub>-\u221e<\/jats:sub>(rather than the usual L<jats:sub>2<\/jats:sub>) norm in the computations. Since L<jats:sub>-\u221e<\/jats:sub>was proved less sensitive to curvature effects, it gives a more accurate estimation of the noise standard deviation compared with Schreiber's results. Here, we illustrate our approach on the H\u00e9non map corrupted by Gaussian white noise with zero mean, as well as on real data obtained from the Nasdaq Composite time series of daily returns.<\/jats:p>","DOI":"10.1142\/s0218127403007965","type":"journal-article","created":{"date-parts":[[2003,9,25]],"date-time":"2003-09-25T03:19:09Z","timestamp":1064459949000},"page":"2309-2313","source":"Crossref","is-referenced-by-count":9,"title":["Large Noise Level Estimation"],"prefix":"10.1142","volume":"13","author":[{"given":"Alexandros","family":"Leontitsis","sequence":"first","affiliation":[{"name":"Center for Research and Applications of Nonlinear Systems, University of Patras, 26500 Patras, Greece"},{"name":"Department of Education, University of Ioannina, 45110 \u2013 Dourouti, Ioannina, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jenny","family":"Pange","sequence":"additional","affiliation":[{"name":"Department of Education, University of Ioannina, 45110 \u2013 Dourouti, Ioannina, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tassos","family":"Bountis","sequence":"additional","affiliation":[{"name":"Center for Research and Applications of Nonlinear Systems, University of Patras, 26500 Patras, Greece"},{"name":"Department of Mathematics, University of Patras, 26500 Patras, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.29.975"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.53.R4263"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.70.3872"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.50.346"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1007\/BF01608556"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127497001023"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.56.1160"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.48.R13"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.56.274"},{"key":"rf11","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1111\/j.2517-6161.1992.tb01885.x","volume":"54","author":"Smith R. L.","journal-title":"J. Roy. Statist. Soc. B"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4076(97)80012-7"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127403007965","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,12,13]],"date-time":"2024-12-13T22:10:45Z","timestamp":1734127845000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127403007965"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,8]]},"references-count":11,"journal-issue":{"issue":"08","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2003,8]]}},"alternative-id":["10.1142\/S0218127403007965"],"URL":"https:\/\/doi.org\/10.1142\/s0218127403007965","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,8]]}}}