{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,29]],"date-time":"2026-07-29T18:42:08Z","timestamp":1785350528013,"version":"3.55.0"},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2000,4,1]],"date-time":"2000-04-01T00:00:00Z","timestamp":954547200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2000,4]]},"abstract":"<jats:p>This paper is concerned with tests in multivariate \ntime series models made up of random walk (with drift) \nand stationary components. When the stationary component \nis white noise, a Lagrange multiplier test of the hypothesis \nthat the covariance matrix of the disturbances driving \nthe multivariate random walk is null is shown to be locally \nbest invariant, something that does not automatically follow \nin the multivariate case. The asymptotic distribution of \nthe test statistic is derived for the general model. The \ntest is then extended to deal with a serially correlated \nstationary component. The main contribution of the paper \nis to propose a test of the validity of a specified value \nfor the rank of the covariance matrix of the disturbances \ndriving the multivariate random walk. This rank is equal \nto the number of common trends, or levels, in the series. \nThe test is very simple insofar as it does not require \nany models to be estimated, even if serial correlation \nis present. Its use with real data is illustrated in the \ncontext of a stochastic volatility model, and the relationship \nwith tests in the cointegration literature is discussed.<\/jats:p>","DOI":"10.1017\/s0266466600162024","type":"journal-article","created":{"date-parts":[[2002,7,27]],"date-time":"2002-07-27T09:45:46Z","timestamp":1027763146000},"page":"176-199","source":"Crossref","is-referenced-by-count":127,"title":["TESTS OF COMMON STOCHASTIC TRENDS"],"prefix":"10.1017","volume":"16","author":[{"given":"Jukka","family":"Nyblom","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Andrew","family":"Harvey","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2000,4,1]]},"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466600162024","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,2]],"date-time":"2019-04-02T15:23:51Z","timestamp":1554218631000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466600162024\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,4]]},"references-count":0,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2000,4]]}},"alternative-id":["S0266466600162024"],"URL":"https:\/\/doi.org\/10.1017\/s0266466600162024","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,4]]}}}