{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,25]],"date-time":"2026-09-25T10:43:39Z","timestamp":1790333019097,"version":"4.1.0"},"reference-count":8,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2010,10,18]],"date-time":"2010-10-18T00:00:00Z","timestamp":1287360000000},"content-version":"unspecified","delay-in-days":8966,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econ Theory"],"published-print":{"date-parts":[[1986,4]]},"abstract":"<jats:p>Under normality, we obtain higher-order approximations to the distributions of the periodogram and related statistics. Our approach is based on the theorem which decomposes the periodogram into the sum of two independent random variables. It is seen that this decomposition enables us to study fairly closely the higher-order properties of not only the periodogram, but also periodogram-based statistics such as the estimators of the spectrum and prediction error variance. Some of the approximation results are graphically presented together with the exact results based on simulations.<\/jats:p>","DOI":"10.1017\/s0266466600011361","type":"journal-article","created":{"date-parts":[[2010,10,18]],"date-time":"2010-10-18T09:14:39Z","timestamp":1287393279000},"page":"33-65","source":"Crossref","is-referenced-by-count":3,"title":["Aproximate Distributions of the Periodogram and Related Statistics under Normality"],"prefix":"10.1017","volume":"2","author":[{"given":"Seiji","family":"Nabeya","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Katsuto","family":"Tanaka","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2010,10,18]]},"reference":[{"key":"S0266466600011361_ref001","volume-title":"The Statistical Analysis of Time Series","author":"Anderson","year":"1971"},{"key":"S0266466600011361_ref005","first-page":"834","article-title":"The estimation of the prediction error variance","volume":"72","author":"Hannan","year":"1977","journal-title":"Journal of the American Statistical Association"},{"key":"S0266466600011361_ref003","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1080\/01621459.1968.11009229","article-title":"Estimation of the innovation variance of a stationary time series","volume":"63","author":"Davis","year":"1968","journal-title":"Journal of the American Statistical Association"},{"key":"S0266466600011361_ref002","doi-asserted-by":"publisher","DOI":"10.1137\/1127088"},{"key":"S0266466600011361_ref007","first-page":"357","article-title":"\u00dcber die asymptotische Verteilung des Periodogramms station\u00e4rer Gaussscher zuf\u00e4lliger Folgen","volume":"9","author":"Wittwer","year":"1978","journal-title":"Mathematische Operationsforschung und Statistik, Series Statistics"},{"key":"S0266466600011361_ref004","doi-asserted-by":"publisher","DOI":"10.1063\/1.3060405"},{"key":"S0266466600011361_ref008","first-page":"361","article-title":"\u00dcber die mehrdimensionalen asymptotischen Verteilungen des Periodogramms Gaussscher station\u00e4rer Folgen","volume":"12","author":"Wittwer","year":"1981","journal-title":"Mathematische Operationsforschung und Statistik, Series Statistics"},{"key":"S0266466600011361_ref006","volume-title":"Distributions in Statistics: Continuous Univariate Distributions-2","author":"Johnson","year":"1970"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466600011361","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,26]],"date-time":"2025-02-26T21:33:28Z","timestamp":1740605608000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466600011361\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1986,4]]},"references-count":8,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1986,4]]}},"alternative-id":["S0266466600011361"],"URL":"https:\/\/doi.org\/10.1017\/s0266466600011361","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[1986,4]]}}}