{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T18:12:52Z","timestamp":1740161572797,"version":"3.37.3"},"reference-count":27,"publisher":"Wiley","license":[{"start":{"date-parts":[[2013,2,20]],"date-time":"2013-02-20T00:00:00Z","timestamp":1361318400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"name":"Funda\u00e7\u00e3o para a Ci\u00eancia e Tecnologia","award":["PTDC\/SAU-ENB\/112294\/2009"],"award-info":[{"award-number":["PTDC\/SAU-ENB\/112294\/2009"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["ISRN Signal Processing"],"published-print":{"date-parts":[[2013,2,20]]},"abstract":"<jats:p>Current measures of causality and temporal precedence have limited frequency and time resolution and therefore may not be viable in the detection of short periods of causality in specific frequencies. In addition, the presence of nonstationarities hinders the causality estimation of current techniques as they are based on Fourier transforms or autoregressive model estimation. In this work we present a combination of techniques to measure causality and temporal precedence between stationary and nonstationary time series, that is sensitive to frequency-specific short episodes of causality. This methodology provides a highly informative time-frequency representation of causality with existing causality measures. This is done by decomposing each time series into intrinsic oscillatory modes with an empirical mode decomposition algorithm and, subsequently, calculating their complex Hilbert spectrum. At each time point the cross-spectrum is calculated between time series and used to measure coherency and compute the transfer function and error covariance matrices using the Wilson-Burg method for spectral factorization. The imaginary part of coherency can then be computed as well as several Granger causality measures in the previous matrices. This work covers the most important theoretical background of these techniques and tries to prove the usefulness of this new approach while pointing out some of its qualities and drawbacks.<\/jats:p>","DOI":"10.1155\/2013\/374064","type":"journal-article","created":{"date-parts":[[2013,2,20]],"date-time":"2013-02-20T22:34:56Z","timestamp":1361399696000},"page":"1-9","source":"Crossref","is-referenced-by-count":6,"title":["Instantaneous Granger Causality with the Hilbert-Huang Transform"],"prefix":"10.1155","volume":"2013","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4492-7767","authenticated-orcid":true,"given":"Jo\u00e3o","family":"Rodrigues","sequence":"first","affiliation":[{"name":"Institute of Biophysics and Biomedical Engineering, Faculty of Sciences, University of Lisbon, Campo Grande, 1749-016  Lisboa, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8107-7338","authenticated-orcid":true,"given":"Alexandre","family":"Andrade","sequence":"additional","affiliation":[{"name":"Institute of Biophysics and Biomedical Engineering, Faculty of Sciences, University of Lisbon, Campo Grande, 1749-016  Lisboa, Portugal"}]}],"member":"311","reference":[{"issue":"1-2","key":"1","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1002\/hbm.460020107","volume":"2","year":"1994","journal-title":"Human Brain Mapping"},{"issue":"3","key":"2","doi-asserted-by":"crossref","first-page":"424","DOI":"10.2307\/1912791","volume":"37","year":"1969","journal-title":"Econometrica"},{"issue":"2","key":"3","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1016\/j.neuroimage.2010.02.059","volume":"58","year":"2011","journal-title":"NeuroImage"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/j.neuroimage.2009.11.060"},{"key":"5","doi-asserted-by":"crossref","first-page":"304","DOI":"10.1080\/01621459.1982.10477803","volume":"77","year":"1982","journal-title":"Journal of the American Statistical Association"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1016\/j.neuroimage.2008.02.020"},{"issue":"1971","key":"7","doi-asserted-by":"crossref","first-page":"903","DOI":"10.1098\/rspa.1998.0193","volume":"454","year":"1998","journal-title":"Proceedings of the Royal Society A"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1109\/LSP.2006.882107"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1186\/1475-925X-9-25"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1007\/s00422-005-0566-y"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1007\/s10827-007-0020-3"},{"issue":"5","key":"13","doi-asserted-by":"crossref","first-page":"503","DOI":"10.1016\/j.sleep.2011.10.035","volume":"13","year":"2012","journal-title":"Sleep Medicine"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1155\/2012\/275073"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1007\/s004220000235"},{"issue":"388","key":"17","doi-asserted-by":"crossref","first-page":"907","DOI":"10.1080\/01621459.1984.10477110","volume":"79","year":"1984","journal-title":"Journal of the American Statistical Association"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1007\/s00422-006-0062-z"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1016\/j.jneumeth.2005.09.001"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1016\/j.jneumeth.2005.06.011"},{"issue":"4","key":"21","doi-asserted-by":"crossref","first-page":"420","DOI":"10.1137\/0123044","volume":"23","year":"1972","journal-title":"SIAM Journal on Applied Mathematics"},{"issue":"23","key":"22","first-page":"1","volume":"100","year":"2008","journal-title":"Physical Review Letters"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1016\/j.clinph.2004.04.029"},{"issue":"1","key":"24","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1142\/S1793536909000047","volume":"1","year":"2009","journal-title":"Advances in Adaptive Data Analysis"},{"key":"25","doi-asserted-by":"publisher","DOI":"10.1109\/LSP.2003.821662"},{"key":"26","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2009.0502"},{"key":"27","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2011.2106779"},{"issue":"4","key":"28","doi-asserted-by":"crossref","first-page":"366","DOI":"10.1109\/TNSRE.2011.2116805","volume":"19","year":"2011","journal-title":"IEEE Transactions on Neural Systems and Rehabilitation Engineering"},{"issue":"5","key":"29","doi-asserted-by":"crossref","first-page":"571","DOI":"10.1109\/TBME.2003.810696","volume":"50","year":"2003","journal-title":"IEEE Transactions on Bio-Medical Engineering"}],"container-title":["ISRN Signal Processing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/archive\/2013\/374064.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/archive\/2013\/374064.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/archive\/2013\/374064.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,12,10]],"date-time":"2020-12-10T09:57:05Z","timestamp":1607594225000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/isrn\/2013\/374064\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,2,20]]},"references-count":27,"alternative-id":["374064","374064"],"URL":"https:\/\/doi.org\/10.1155\/2013\/374064","relation":{},"ISSN":["2090-505X"],"issn-type":[{"type":"electronic","value":"2090-505X"}],"subject":[],"published":{"date-parts":[[2013,2,20]]}}}