{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T16:11:13Z","timestamp":1775146273211,"version":"3.50.1"},"reference-count":118,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","license":[{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Access"],"published-print":{"date-parts":[[2023]]},"DOI":"10.1109\/access.2023.3307628","type":"journal-article","created":{"date-parts":[[2023,8,29]],"date-time":"2023-08-29T17:57:21Z","timestamp":1693331841000},"page":"94442-94478","source":"Crossref","is-referenced-by-count":25,"title":["Tutorial on Empirical Mode Decomposition: Basis Decomposition and Frequency Adaptive Graduation in Non-Stationary Time Series"],"prefix":"10.1109","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1831-8351","authenticated-orcid":false,"given":"Cole","family":"van Jaarsveldt","sequence":"first","affiliation":[{"name":"Department of Actuarial Mathematics &#x0026; Statistics, Heriot-Watt University, Edinburgh, U.K."}]},{"given":"Gareth W.","family":"Peters","sequence":"additional","affiliation":[{"name":"Department of Statistics and Applied Probability, University of California at Santa Barbara, Santa Barbara, CA, USA"}]},{"given":"Matthew","family":"Ames","sequence":"additional","affiliation":[{"name":"ResilientML, Melbourne, VIC, Australia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8381-1751","authenticated-orcid":false,"given":"Mike","family":"Chantler","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Heriot-Watt University, Edinburgh, U.K."}]}],"member":"263","reference":[{"key":"ref57","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0025-3_1"},{"key":"ref56","doi-asserted-by":"publisher","DOI":"10.1109\/TASSP.1977.1162950"},{"key":"ref59","author":"bowman","year":"2017","journal-title":"Nonparametric smoothing lecture notes"},{"key":"ref58","doi-asserted-by":"crossref","first-page":"585","DOI":"10.1109\/PROC.1970.7696","article-title":"the discrete hilbert transform","volume":"58","author":"kak","year":"1970","journal-title":"Proceedings of the IEEE"},{"key":"ref53","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfineco.2014.10.010"},{"key":"ref52","doi-asserted-by":"publisher","DOI":"10.1016\/0304-405X(93)90023-5"},{"key":"ref55","first-page":"548","article-title":"&#x2018;Instantaneous&#x2019; frequency","volume":"41","author":"shekel","year":"1953","journal-title":"Proc Inst Radio Eng"},{"key":"ref54","doi-asserted-by":"publisher","DOI":"10.1109\/ACCESS.2021.3117080"},{"key":"ref51","first-page":"1022","article-title":"Multi-interval discretization of continuous-valued attributes for classification learning","volume":"2","author":"fayyad","year":"1993","journal-title":"Proc 13th Int Joint Conf Artif Intell"},{"key":"ref50","doi-asserted-by":"publisher","DOI":"10.1016\/S0893-6080(00)00026-5"},{"key":"ref46","doi-asserted-by":"publisher","DOI":"10.1016\/j.oceaneng.2004.03.007"},{"key":"ref45","doi-asserted-by":"publisher","DOI":"10.1016\/j.asr.2003.02.045"},{"key":"ref48","doi-asserted-by":"publisher","DOI":"10.1007\/BF02900475"},{"key":"ref47","first-page":"53","article-title":"Identification of oscillations in historical global streamflow data using empirical mode decomposition","author":"chiew","year":"2005","journal-title":"Regional Hydrological Impacts Climatic Change&#x2014;Hydroclimatic Variabiltiy"},{"key":"ref42","first-page":"8","article-title":"On empirical mode decomposition and its algorithms","volume":"3","author":"rilling","year":"2003","journal-title":"Proc IEEE Workshop Nonlinear Signal Image Process (EURASIP)"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1631\/jzus.2001.0247"},{"key":"ref44","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsv.2008.01.020"},{"key":"ref43","first-page":"4258","article-title":"A simple boundary process technique for empirical mode decomposition","author":"zeng","year":"2004","journal-title":"Proc IEEE Int Geosci Remote Sens Symp"},{"key":"ref49","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0173857"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1111\/1467-842X.00187"},{"key":"ref7","article-title":"X11 time series decomposition and sampling errors","author":"sutcliffe","year":"1993"},{"key":"ref9","article-title":"The X-11-ARIMA seasonal adjustment method","author":"dagum","year":"1980"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1201\/9781420027532"},{"key":"ref3","author":"huang","year":"1999","journal-title":"Computer implemented empirical mode decomposition method apparatus and article of manufacture"},{"key":"ref6","article-title":"The X-11 variant of the census method II seasonal adjustment program","author":"shiskin","year":"1967"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1029\/2007RG000228"},{"key":"ref100","doi-asserted-by":"publisher","DOI":"10.6339\/JDS.2007.05(2).396"},{"key":"ref101","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2013.2265222"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-6333-3"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1142\/S1793536914500113"},{"key":"ref34","author":"hyndman","year":"2018","journal-title":"Forecasting Principles and Practice"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-39348-8_33"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.2307\/2371268"},{"key":"ref31","first-page":"536","article-title":"On the theory of filter amplifiers","volume":"7","author":"butterworth","year":"1930","journal-title":"The Wireless Engineer and Experimental Wireless"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1162\/003465303765299774"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466608080389"},{"key":"ref32","author":"miller","year":"1946","journal-title":"Elements of Graduation"},{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1007\/s10444-004-7614-3"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.1109\/ICASSP.2007.367107"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1214\/13-AOS1189"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1137\/070690274"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1080\/10618600.2015.1054033"},{"key":"ref25","first-page":"1042","article-title":"Trend filtering on graphs","volume":"38","author":"wang","year":"2015","journal-title":"Proc 18th Int Conf Artif Intell Statist (AISTATS)"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1198\/073500107000000322"},{"key":"ref22","first-page":"3","article-title":"STL: A seasonal-trend decomposition procedure based on loess","volume":"6","author":"robert","year":"1990","journal-title":"J Offic Statist"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.2307\/2636257"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.2307\/2953682"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1017\/S0020268100042633"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1115\/1.3662552"},{"key":"ref13","first-page":"43","article-title":"Note on graduation by adjusted average","volume":"17","author":"henderson","year":"1916","journal-title":"Trans Actuarial Soc Amer"},{"key":"ref12","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1080\/07350015.1998.10524743","article-title":"New capabilities and methods of the X-12-ARIMA seasonal-adjustment program","volume":"16","author":"findley","year":"1998","journal-title":"J Bus Econ Statist"},{"key":"ref15","first-page":"29","article-title":"A new method of graduation","volume":"25","author":"henderson","year":"1924","journal-title":"Trans Actuarial Soc Amer"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1017\/S0013091500077853"},{"key":"ref97","doi-asserted-by":"publisher","DOI":"10.4324\/9781351140645"},{"key":"ref96","first-page":"645","article-title":"Gaussian processes with monotonicity information","author":"riihim\u00e4ki","year":"2010","journal-title":"Proc 13th Int Conf Artif Intell Statist"},{"key":"ref11","first-page":"77","article-title":"A new method to reduce unwanted ripples and revisions in trend-cycle estimates from X11ARIMA","volume":"22","author":"dagum","year":"1996","journal-title":"Survey Methodology"},{"key":"ref99","doi-asserted-by":"publisher","DOI":"10.1016\/0165-1684(94)90029-9"},{"key":"ref10","article-title":"The X-11-ARIMA\/88 seasonal adjustment method: Foundations and user&#x2019;s manual","author":"dagum","year":"1988","journal-title":"Time Series Research and Analysis Division"},{"key":"ref98","doi-asserted-by":"publisher","DOI":"10.1016\/0165-1684(91)90079-X"},{"key":"ref17","author":"musgrave","year":"1964","journal-title":"Alternative sets of weights for proposed X-11 seasonal factor curve moving averages"},{"key":"ref16","author":"musgrave","year":"1964","journal-title":"A set of end weights to end all end weights"},{"key":"ref19","first-page":"1","article-title":"Local polynomial trend-cycle predictors in reproducing kernel Hilbert spaces for current economic analysis","author":"dagum","year":"2006","journal-title":"Anales de Economi?a Aplicada"},{"key":"ref18","article-title":"Trend-cycle estimation in reproducing kernel Hilbert spaces","author":"bianconcini","year":"2006"},{"key":"ref93","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(71)90184-3"},{"key":"ref92","first-page":"2507","article-title":"When is there a representer theorem? Vector versus matrix regularizers","volume":"10","author":"argyriou","year":"2009","journal-title":"J Mach Learn Res"},{"key":"ref95","doi-asserted-by":"publisher","DOI":"10.1111\/j.2517-6161.1978.tb01050.x"},{"key":"ref94","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0020217"},{"key":"ref91","author":"sch\u00f6lkopf","year":"2002","journal-title":"Learning With Kernels Support Vector Machines Regularization Optimization and Beyond"},{"key":"ref90","author":"saitoh","year":"1988","journal-title":"Theory of Reproducing Kernels and Its Applications"},{"key":"ref89","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1950-0051437-7"},{"key":"ref86","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1016\/j.ymssp.2012.09.015","article-title":"A review on empirical mode decomposition in fault diagnosis of rotating machinery","volume":"35","author":"lei","year":"2013","journal-title":"Mech Syst Signal Process"},{"key":"ref85","first-page":"891","article-title":"Damage detection using empirical mode decomposition method and a comparison with wavelet analysis","author":"vincent","year":"1999","journal-title":"Proc 2nd Int Workshop Struct Health Monitor"},{"key":"ref88","doi-asserted-by":"publisher","DOI":"10.7551\/mitpress\/3206.001.0001"},{"key":"ref87","doi-asserted-by":"publisher","DOI":"10.1109\/ICASSP.2005.1416051"},{"key":"ref82","doi-asserted-by":"publisher","DOI":"10.5351\/KJAS.2009.22.3.499"},{"key":"ref81","doi-asserted-by":"publisher","DOI":"10.1016\/j.eneco.2007.02.012"},{"key":"ref84","doi-asserted-by":"publisher","DOI":"10.2299\/jsp.17.215"},{"key":"ref83","doi-asserted-by":"publisher","DOI":"10.1109\/ICSCS.2008.4746883"},{"key":"ref80","doi-asserted-by":"publisher","DOI":"10.1109\/IEMBS.2006.259340"},{"key":"ref79","first-page":"1","article-title":"Denoising via empirical mode decomposition","volume":"4","author":"boudraa","year":"2006","journal-title":"Proc IEEE Int Symp Control"},{"key":"ref108","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2007.901155"},{"key":"ref78","first-page":"1581","article-title":"Detrending and denoising with empirical mode decompositions","author":"flandrin","year":"2004","journal-title":"Proc 12th Eur Signal Process Conf"},{"key":"ref109","doi-asserted-by":"publisher","DOI":"10.1142\/S1793536909000047"},{"key":"ref106","first-page":"153","article-title":"Wavelet analysis and signal processing","author":"coifman","year":"1992","journal-title":"Wavelets and Their Applications"},{"key":"ref107","doi-asserted-by":"publisher","DOI":"10.1109\/SSP.2007.4301354"},{"key":"ref75","doi-asserted-by":"publisher","DOI":"10.1007\/BF02162161"},{"key":"ref104","doi-asserted-by":"publisher","DOI":"10.1109\/TASSP.1984.1164317"},{"key":"ref74","doi-asserted-by":"publisher","DOI":"10.1016\/j.mcm.2013.04.007"},{"key":"ref105","doi-asserted-by":"publisher","DOI":"10.1016\/0016-7142(84)90025-5"},{"key":"ref77","author":"fourier","year":"1822","journal-title":"La Th&#x00E9 orie Analytique de la Chaleur"},{"key":"ref102","article-title":"Empirical Fourier decomposition","author":"zhou","year":"2019","journal-title":"arXiv 1912 00414"},{"key":"ref76","doi-asserted-by":"publisher","DOI":"10.1214\/ss\/1038425655"},{"key":"ref103","doi-asserted-by":"publisher","DOI":"10.1016\/j.mcm.2004.02.032"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1146\/annurev.fluid.31.1.417"},{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1998.0193"},{"key":"ref71","doi-asserted-by":"publisher","DOI":"10.1038\/141183a0"},{"key":"ref111","year":"2020","journal-title":"Trends in atmospheric carbon dioxide"},{"key":"ref70","article-title":"A product theorem for Hilbert transforms","author":"bedrosian","year":"1962"},{"key":"ref112","doi-asserted-by":"publisher","DOI":"10.1002\/asmb.501"},{"key":"ref73","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2019.104983"},{"key":"ref72","doi-asserted-by":"publisher","DOI":"10.1017\/S1748499523000088"},{"key":"ref110","first-page":"77","article-title":"Portfolio selection","volume":"7","author":"markowitz","year":"1952","journal-title":"J Finance"},{"key":"ref68","author":"schwartz","year":"1966","journal-title":"Communication Systems and Techniques"},{"key":"ref67","author":"bendat","year":"1986","journal-title":"Random Data Analysis and Measurement Procedures"},{"key":"ref117","doi-asserted-by":"publisher","DOI":"10.2139\/ssrn.4373433"},{"key":"ref69","doi-asserted-by":"publisher","DOI":"10.1049\/ji-3-2.1946.0074"},{"key":"ref118","doi-asserted-by":"publisher","DOI":"10.2139\/ssrn.4449044"},{"key":"ref64","doi-asserted-by":"publisher","DOI":"10.1109\/5.135376"},{"key":"ref115","year":"2021","journal-title":"Yahoo! finance"},{"key":"ref63","doi-asserted-by":"publisher","DOI":"10.1186\/s12874-019-0666-3"},{"key":"ref116","doi-asserted-by":"publisher","DOI":"10.2139\/ssrn.4233231"},{"key":"ref66","author":"cohen","year":"1995","journal-title":"Time-Frequency Analysis"},{"key":"ref113","first-page":"425","article-title":"Capital asset prices: A theory of market equilibrium under conditions of risk","volume":"19","author":"sharpe","year":"1964","journal-title":"J Finance"},{"key":"ref65","doi-asserted-by":"publisher","DOI":"10.1109\/5.135378"},{"key":"ref114","first-page":"587","article-title":"Security prices, risk, and maximal gains from diversification","volume":"20","author":"lintner","year":"1965","journal-title":"J Finance"},{"key":"ref60","doi-asserted-by":"publisher","DOI":"10.1007\/BF01404567"},{"key":"ref62","doi-asserted-by":"publisher","DOI":"10.1109\/IECBES.2016.7843518"},{"key":"ref61","author":"wahba","year":"1987","journal-title":"Spline Models for Observational Data"}],"container-title":["IEEE Access"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx7\/6287639\/10005208\/10234222.pdf?arnumber=10234222","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,27]],"date-time":"2024-10-27T01:54:01Z","timestamp":1729994041000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/10234222\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023]]},"references-count":118,"URL":"https:\/\/doi.org\/10.1109\/access.2023.3307628","relation":{},"ISSN":["2169-3536"],"issn-type":[{"value":"2169-3536","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023]]}}}