{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,8]],"date-time":"2026-02-08T02:45:31Z","timestamp":1770518731399,"version":"3.49.0"},"reference-count":8,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[1952,1,1]],"date-time":"1952-01-01T00:00:00Z","timestamp":-568080000000},"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":[[1952,1,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n               <jats:p>Quenouille (1947), and Bartlett and Diananda (1950), have given large sample goodness-of-fit tests of the hypothesis that a time series can be represented by a linear autoregressive scheme with independent residuals. Asymptotic power functions of these tests are derived for alternative hypotheses specified by linear autoregressive schemes of higher order with independent residuals, and of the same or higher order with residuals among which there exists dependence of finite extent. On the null hypothesis, the constants of the scheme may either be given a priori, or be unspecified, having to be estimated from the data. Both these cases are considered in a detailed comparison of the asymptotic power functions for the two types of test. It is shown how, in the first case, the Quenouille tests may be conveniently modified to give greater power. A discussion is given of the application of the likelihood-ratio method for obtaining large sample tests, and of its relation to the Quenouille tests when the residuals are normally distributed.<\/jats:p>","DOI":"10.1111\/j.2517-6161.1952.tb00106.x","type":"journal-article","created":{"date-parts":[[2018,12,7]],"date-time":"2018-12-07T06:24:05Z","timestamp":1544163845000},"page":"117-134","source":"Crossref","is-referenced-by-count":20,"title":["Some Properties of the Asymptotic Power Functions of Goodness-of-Fit Tests for Linear Autoregressive Schemes"],"prefix":"10.1093","volume":"14","author":[{"given":"A. M.","family":"Walker","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Manchester"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2018,12,5]]},"reference":[{"key":"2024090920090032400_cit1","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1111\/j.2517-6161.1950.tb00047.x","article-title":"Extensions of Quenouille\u2019s test for autoregressive schemes","volume":"12","author":"Bartlett","year":"1950","journal-title":"J. Roy. Statist. Soc., B"},{"key":"2024090920090032400_cit2","volume-title":"M.Sc. Thesis","author":"Lee","year":"1951"},{"key":"2024090920090032400_cit3","doi-asserted-by":"crossref","first-page":"173","DOI":"10.2307\/1905674","article-title":"On the statistical treatment of linear stochastic difference equations","volume":"11","author":"Mann","year":"1943","journal-title":"Econometrica"},{"key":"2024090920090032400_cit4","doi-asserted-by":"crossref","first-page":"123","DOI":"10.2307\/2981315","article-title":"A large-sample test for the goodness of fit of autoregressive schemes","volume":"110","author":"Quenouille","year":"1947","journal-title":"J. Roy. Statist. Soc., A"},{"key":"2024090920090032400_cit5","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1111\/j.2517-6161.1949.tb00023.x","article-title":"Approximate tests of correlation in time series","volume":"11","author":"Quenouille","year":"1949","journal-title":"J. Roy. Statist. Soc., B"},{"key":"2024090920090032400_cit6","doi-asserted-by":"crossref","first-page":"102","DOI":"10.1111\/j.2517-6161.1950.tb00046.x","article-title":"A note on a generalisation of the large sample goodness-of-fit test for linear autoregressive schemes","volume":"12","author":"Walker","year":"1950","journal-title":"J. Roy. Statist. Soc., B"},{"key":"2024090920090032400_cit7","volume-title":"Hypothesis Testing in Time Series Analysis.","author":"Whittle","year":"1951"},{"key":"2024090920090032400_cit8","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1111\/j.2517-6161.1949.tb00036.x","article-title":"A large-sample test for moving averages","volume":"11","author":"Wold","year":"1949","journal-title":"J. Roy. Statist. Soc., B"}],"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.2517-6161.1952.tb00106.x","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/14\/1\/117\/49093744\/jrsssb_14_1_117.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/14\/1\/117\/49093744\/jrsssb_14_1_117.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,9]],"date-time":"2024-09-09T20:15:42Z","timestamp":1725912942000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/14\/1\/117\/7026608"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1952,1,1]]},"references-count":8,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2018,12,5]]},"published-print":{"date-parts":[[1952,1,1]]}},"URL":"https:\/\/doi.org\/10.1111\/j.2517-6161.1952.tb00106.x","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"value":"1369-7412","type":"print"},{"value":"1467-9868","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[1952,1]]},"published":{"date-parts":[[1952,1,1]]}}}