{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T14:47:25Z","timestamp":1762008445797,"version":"build-2065373602"},"reference-count":11,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[1983,9,1]],"date-time":"1983-09-01T00:00:00Z","timestamp":431222400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[1983,9,1]]},"abstract":"<jats:title>SUMMARY<\/jats:title>\n               <jats:p>Consider a scalar linear process {xt} whose spectral density is \u03c3 \u00a02 \u00a0k(\u03bb, \u03b8 \u00a00) where \u03c32 is the innovation variance and k(\u22c5,\u03b80)\u2208{k(\u22c5,\u03b8):\u03b8\u2208S\u2282\u211dq}. We introduce a class of estimators of \u03b80 based only on the sample autocorrelations. These estimators are shown to be consistent and asymptotically normally distributed with a covariance matrix which is independent of the distributions of the innovations. A lower bound to the asymptotic covariances of these estimators is derived and is shown to be achieved by the least-squares estimator. We also consider the extent to which these results generalize to the multivariate case. In particular, we present a multivariate generalization of the main result presented by Kabaila (1980).<\/jats:p>","DOI":"10.1111\/j.2517-6161.1983.tb01237.x","type":"journal-article","created":{"date-parts":[[2018,12,7]],"date-time":"2018-12-07T06:45:41Z","timestamp":1544165141000},"page":"107-119","source":"Crossref","is-referenced-by-count":2,"title":["On Estimating Time Series Parameters Using Sample Autocorrelations"],"prefix":"10.1093","volume":"45","author":[{"given":"Paul","family":"Kabaila","sequence":"first","affiliation":[{"name":"CSIRO , South Melbourne , Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2018,12,5]]},"reference":[{"key":"2024090920511828700_rssb01237-cit-0001","doi-asserted-by":"crossref","first-page":"1545","DOI":"10.1214\/aoms\/1177700378","article-title":"On Fisher's bound for asymptotic variances","volume":"35","author":"Bahadur","year":"1964","journal-title":"Ann. Math. Statist."},{"key":"2024090920511828700_rssb01237-cit-0002","doi-asserted-by":"crossref","first-page":"469","DOI":"10.2307\/1425830","article-title":"Asymptotic inference in stationary Gaussian processes","volume":"5","author":"Davies","year":"1973","journal-title":"Adv. Appl. Prob."},{"key":"2024090920511828700_rssb01237-cit-0003","doi-asserted-by":"crossref","DOI":"10.1016\/0304-4149(83)90005-4","article-title":"A central limit theorem for estimation in Gaussian stationary time series observed at unequally spaced times","volume-title":"Stoch. Proc. Appl.","author":"Dunsmuir","year":"1983"},{"key":"2024090920511828700_rssb01237-cit-0004","doi-asserted-by":"crossref","first-page":"339","DOI":"10.2307\/1425908","article-title":"Vector linear time series models","volume":"8","author":"Dunsmuir","year":"1976","journal-title":"Adv. Appl. Prob."},{"key":"2024090920511828700_rssb01237-cit-0005","doi-asserted-by":"crossref","first-page":"306","DOI":"10.1093\/biomet\/46.3-4.306","article-title":"Efficient estimation of parameters in moving-average models","volume":"46","author":"Durbin","year":"1959","journal-title":"Biometrika"},{"key":"2024090920511828700_rssb01237-cit-0006","doi-asserted-by":"crossref","first-page":"130","DOI":"10.2307\/3212501","article-title":"The asymptotic theory of linear time-series models","volume":"10","author":"Hannan","year":"1973","journal-title":"J. Appl. Prob."},{"key":"2024090920511828700_rssb01237-cit-0007","doi-asserted-by":"crossref","first-page":"2058","DOI":"10.1214\/aoms\/1177690885","article-title":"On limit theorems for quadratic forms of discrete time-series","volume":"43","author":"Hannan","year":"1972","journal-title":"Ann. Math. Statist."},{"key":"2024090920511828700_rssb01237-cit-0008","doi-asserted-by":"crossref","first-page":"1082","DOI":"10.1214\/aos\/1176345145","article-title":"An optimality property of the least-squares estimate of the parameter of the spectrum of a purely non-deterministic time-series","volume":"8","author":"Kabaila","year":"1980","journal-title":"Ann. Statist."},{"key":"2024090920511828700_rssb01237-cit-0009","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1007\/BF02590998","article-title":"Estimation and information in stationary time-series","volume":"2","author":"Whittle","year":"1953","journal-title":"Ark. Mat."},{"key":"2024090920511828700_rssb01237-cit-0010","article-title":"Some recent contributions to the theory of stationary processes. Appendix 2 of Wold, H","volume-title":"A Study in the Analysis of Stationary Time Series.","author":"Whittle","year":"1954"},{"key":"2024090920511828700_rssb01237-cit-0011","first-page":"105","article-title":"Gaussian estimation in stationary time series","volume":"39","author":"Whittle","year":"1962","journal-title":"Bull. Int. Statist. Inst."}],"container-title":["Journal of the Royal Statistical Society Series B: Statistical Methodology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1111%2Fj.2517-6161.1983.tb01237.x","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/45\/1\/107\/49097798\/jrsssb_45_1_107.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/45\/1\/107\/49097798\/jrsssb_45_1_107.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,9]],"date-time":"2024-09-09T21:38:25Z","timestamp":1725917905000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/45\/1\/107\/7027704"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1983,9,1]]},"references-count":11,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2018,12,5]]},"published-print":{"date-parts":[[1983,9,1]]}},"URL":"https:\/\/doi.org\/10.1111\/j.2517-6161.1983.tb01237.x","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"type":"print","value":"1369-7412"},{"type":"electronic","value":"1467-9868"}],"subject":[],"published-other":{"date-parts":[[1983,9]]},"published":{"date-parts":[[1983,9,1]]}}}