{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,4]],"date-time":"2026-10-04T14:57:45Z","timestamp":1791125865253,"version":"4.1.0"},"reference-count":42,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2009,6,12]],"date-time":"2009-06-12T00:00:00Z","timestamp":1244764800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"publisher","award":["IR01GM072876:01A1"],"award-info":[{"award-number":["IR01GM072876:01A1"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2009,9,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>We propose a general bootstrap procedure to approximate the null distribution of non-parametric frequency domain tests about the spectral density matrix of a multivariate time series. Under a set of easy-to-verify conditions, we establish asymptotic validity of the bootstrap procedure proposed. We apply a version of this procedure together with a new statistic to test the hypothesis that the spectral densities of not necessarily independent time series are equal. The test statistic proposed is based on an L2-distance between the non-parametrically estimated individual spectral densities and an overall, \u2018pooled\u2019 spectral density, the latter being obtained by using the whole set of m time series considered. The effects of the dependence between the time series on the power behaviour of the test are investigated. Some simulations are presented and a real life data example is discussed.<\/jats:p>","DOI":"10.1111\/j.1467-9868.2009.00709.x","type":"journal-article","created":{"date-parts":[[2009,6,12]],"date-time":"2009-06-12T14:52:11Z","timestamp":1244818331000},"page":"831-857","source":"Crossref","is-referenced-by-count":49,"title":["Bootstrapping Frequency Domain Tests in Multivariate Time Series with an Application to Comparing Spectral Densities"],"prefix":"10.1093","volume":"71","author":[{"given":"Holger","family":"Dette","sequence":"first","affiliation":[{"name":"Ruhr-Universit\u00e4t Bochum , Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Efstathios","family":"Paparoditis","sequence":"additional","affiliation":[{"name":"University of Cyprus , Nicosia , Cyprus"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2009,6,12]]},"reference":[{"key":"2023032921301918700_","first-page":"849","article-title":"Nested reduced-rank autoregressive models for multiple time series","volume":"83","author":"Ahn","year":"1988","journal-title":"J. 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