{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,8]],"date-time":"2025-02-08T06:10:25Z","timestamp":1738995025842,"version":"3.37.0"},"reference-count":37,"publisher":"Cambridge University Press (CUP)","issue":"5","license":[{"start":{"date-parts":[[2009,2,11]],"date-time":"2009-02-11T00:00:00Z","timestamp":1234310400000},"content-version":"unspecified","delay-in-days":4455,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[1996,12]]},"abstract":"<jats:p>This paper provides limit theorems for spectral density matrix estimators and functionals of it for a bivariate covariance stationary process whose spectral density matrix has singularities not only at the origin but possibly at some other frequencies and, thus, applies to time series exhibiting long memory. In particular, we show that the consistency and asymptotic normality of the spectral density matrix estimator at a frequency, say \u03bb, which hold for weakly dependent time series, continue to hold for long memory processes when \u03bb lies outside any arbitrary neighborhood of the singularities. Specifically, we show that for the standard properties of spectral density matrix estimators to hold, only local smoothness of the spectral density matrix is required in a neighborhood of the frequency in which we are interested. Therefore, we are able to relax, among other conditions, the absolute summability of the autocovariance function and of the fourth-order cumulants or summability conditions on mixing coefficients, assumed in much of the literature, which imply that the spectral density matrix is globally smooth and bounded.<\/jats:p>","DOI":"10.1017\/s0266466600007155","type":"journal-article","created":{"date-parts":[[2009,3,10]],"date-time":"2009-03-10T15:38:09Z","timestamp":1236699489000},"page":"773-792","source":"Crossref","is-referenced-by-count":4,"title":["Spectral Analysis for Bivariate Time Series with Long Memory"],"prefix":"10.1017","volume":"12","author":[{"given":"J.","family":"Hidalgo","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2009,2,11]]},"reference":[{"volume-title":"Analysis of Economic Time Series","year":"1979","author":"Nerlove","key":"S0266466600007155_ref024"},{"key":"S0266466600007155_ref023","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176345696"},{"key":"S0266466600007155_ref021","doi-asserted-by":"publisher","DOI":"10.1007\/BF01192551"},{"key":"S0266466600007155_ref020","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/68.1.165"},{"key":"S0266466600007155_ref017","doi-asserted-by":"publisher","DOI":"10.1002\/9780470316429"},{"volume-title":"Asymptotic Behaviour of Trigonometric Series","year":"1974","author":"Yong","key":"S0266466600007155_ref037"},{"key":"S0266466600007155_ref016","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/50.3-4.293"},{"key":"S0266466600007155_ref010","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(80)90092-5"},{"key":"S0266466600007155_ref002","first-page":"3","article-title":"Confidence intervals for the crossvariance function","volume":"5","author":"Brillinger","year":"1979","journal-title":"Selecla Statistica Canadian"},{"key":"S0266466600007155_ref014","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9892.1989.tb00026.x"},{"key":"S0266466600007155_ref013","doi-asserted-by":"publisher","DOI":"10.2307\/2974408"},{"volume-title":"Introduction to Statistical Time Series","year":"1976","author":"Fuller","key":"S0266466600007155_ref007"},{"volume-title":"Time Series. 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