{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T11:57:06Z","timestamp":1759147026745},"reference-count":24,"publisher":"Oxford University Press (OUP)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019,5,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n               <jats:p>We investigate the collinearity of vector time series in the frequency domain, by examining the rank of the spectral density matrix at a given frequency of interest. Rank reduction corresponds to collinearity at the given frequency. When the time series is nonstationary and has been differenced to stationarity, collinearity corresponds to co-integration at a particular frequency. We examine rank through the Schur complements of the spectral density matrix, testing for rank reduction via assessing the positivity of these Schur complements, which are obtained from a nonparametric estimator of the spectral density. New asymptotic results for the test statistics are derived under the fixed bandwidth ratio paradigm; they diverge under the alternative, but under the null hypothesis of collinearity the test statistics converge to a non-standard limiting distribution. Subsampling is used to obtain the limiting null quantiles. A simulation study and an empirical illustration for 6-variate time series data are provided.<\/jats:p>","DOI":"10.1093\/ectj\/uty002","type":"journal-article","created":{"date-parts":[[2019,1,29]],"date-time":"2019-01-29T07:58:24Z","timestamp":1548748704000},"page":"97-116","source":"Crossref","is-referenced-by-count":6,"title":["Testing collinearity of vector time series"],"prefix":"10.1093","volume":"22","author":[{"given":"Tucker S","family":"McElroy","sequence":"first","affiliation":[{"name":"U.S. Census Bureau, Associate Directorate for Research and Methodology, 4600 Silver Hill Road, Washington, DC 20233"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Agnieszka","family":"Jach","sequence":"additional","affiliation":[{"name":"Department of Finance and Statistics, Hanken School of Economics, Helsinki, 4600 Silver Hill Road, Washington, DC 20233, 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