{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,25]],"date-time":"2026-09-25T10:43:01Z","timestamp":1790332981035,"version":"4.1.0"},"reference-count":37,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2017,2,27]],"date-time":"2017-02-27T00:00:00Z","timestamp":1488153600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["www.cambridge.org"],"crossmark-restriction":true},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2018,2]]},"abstract":"<jats:p>We derive uniform convergence results of lag-window spectral density estimates for a general class of multivariate stationary processes represented by an arbitrary measurable function of iid innovations. Optimal rates of convergence, that hold as both the time series and the cross section dimensions diverge, are obtained under mild and easily verifiable conditions. Our theory complements earlier results, most of which are univariate, which primarily concern in-probability, weak or distributional convergence, yet under a much stronger set of regularity conditions, such as linearity in iid innovations. Based on cross spectral density functions, we then propose a new test for independence between two stationary time series. We also explain the extent to which our results provide the foundation to derive the double asymptotic results for estimation of generalized dynamic factor models.<\/jats:p>","DOI":"10.1017\/s0266466617000068","type":"journal-article","created":{"date-parts":[[2017,2,27]],"date-time":"2017-02-27T01:11:43Z","timestamp":1488157903000},"page":"1-22","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":30,"title":["ASYMPTOTIC THEORY FOR SPECTRAL DENSITY ESTIMATES OF GENERAL MULTIVARIATE TIME SERIES"],"prefix":"10.1017","volume":"34","author":[{"given":"Wei Biao","family":"Wu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Paolo","family":"Zaffaroni","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2017,2,27]]},"reference":[{"key":"S0266466617000068_ref31","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198522249.001.0001","volume-title":"Non-linear Time Series: A Dynamical System Approach","author":"Tong","year":"1990"},{"key":"S0266466617000068_ref22","doi-asserted-by":"crossref","first-page":"985","DOI":"10.1016\/j.jspi.2006.06.033","article-title":"Long run variance estimation and robust regression testing using sharp origin kernels with no truncation","volume":"137","author":"Phillips","year":"2007","journal-title":"Journal of Statistical Planning and Inference"},{"key":"S0266466617000068_ref32","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1017\/S0266466601173019","article-title":"Edgeworth expansions for spectral density estimates and Studentized sample mean","volume":"17","author":"Velasco","year":"2001","journal-title":"Econometric Theory"},{"key":"S0266466617000068_ref20","doi-asserted-by":"crossref","first-page":"745","DOI":"10.1214\/aop\/1176994938","article-title":"Large deviations of sums of independent random variables","volume":"7","author":"Nagaev","year":"1979","journal-title":"Annals of Probabability"},{"key":"S0266466617000068_ref30","doi-asserted-by":"crossref","first-page":"1167","DOI":"10.1198\/016214502388618960","article-title":"Forecasting using principal components from a large number of predictors","volume":"97","author":"Stock","year":"2002b","journal-title":"Journal of the American Statistical Association"},{"key":"S0266466617000068_ref34","doi-asserted-by":"crossref","unstructured":"Xiao, H. & Wu, W.B. 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