{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,9]],"date-time":"2026-10-09T07:29:10Z","timestamp":1791530950389,"version":"4.3.4"},"reference-count":30,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2015,12,14]],"date-time":"2015-12-14T00:00:00Z","timestamp":1450051200000},"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":[[2017,2]]},"abstract":"<jats:p>The behavior of the power function of autocorrelation tests such as the Durbin\u2013Watson test in time series regressions or the Cliff-Ord test in spatial regression models has been intensively studied in the literature. When the correlation becomes strong, Kr\u00e4mer (1985, <jats:italic>Journal of Econometrics<\/jats:italic> 28, 363\u2013370.) (for the Durbin\u2013Watson test) and Kr\u00e4mer (2005, <jats:italic>Journal of Statistical Planning and Inference<\/jats:italic>, 128, 489\u2013496) (for the Cliff-Ord test) have shown that power can be very low, in fact can converge to zero, under certain circumstances. Motivated by these results, Martellosio (2010, <jats:italic>Econometric Theory<\/jats:italic>, 26, 152\u2013186) set out to build a general theory that would explain these findings. Unfortunately, Martellosio (2010) does not achieve this goal, as a substantial portion of his results and proofs suffer from nontrivial flaws. The present paper now builds a theory as envisioned in Martellosio (2010) in an even more general framework, covering general invariant tests of a hypothesis on the disturbance covariance matrix in a linear regression model. The general results are then specialized to testing for spatial correlation and to autocorrelation testing in time series regression models. We also characterize the situation where the null and the alternative hypothesis are indistinguishable by invariant tests.<\/jats:p>","DOI":"10.1017\/s026646661500033x","type":"journal-article","created":{"date-parts":[[2015,12,14]],"date-time":"2015-12-14T08:35:04Z","timestamp":1450082104000},"page":"1-68","source":"Crossref","is-referenced-by-count":3,"title":["ON THE POWER OF INVARIANT TESTS FOR HYPOTHESES ON A COVARIANCE MATRIX"],"prefix":"10.1017","volume":"33","author":[{"given":"David","family":"Preinerstorfer","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Benedikt M.","family":"P\u00f6tscher","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2015,12,14]]},"reference":[{"key":"S026646661500033X_ref2","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1080\/01621459.1979.10481637","article-title":"Linear models with exchangeably distributed errors","volume":"74","author":"Arnold","year":"1979","journal-title":"Journal of the American Statistical Association"},{"key":"S026646661500033X_ref30","doi-asserted-by":"crossref","first-page":"3907","DOI":"10.1080\/03610928908830130","article-title":"On the power of the Durbin-Watson test under high autocorrelation","volume":"18","author":"Zeisel","year":"1989","journal-title":"Communications in Statistics-Theory and Methods"},{"key":"S026646661500033X_ref9","doi-asserted-by":"crossref","first-page":"701","DOI":"10.1080\/01621459.1980.10477536","article-title":"Note on a condition for equality of sample variances in a linear model","volume":"75","author":"Kariya","year":"1980","journal-title":"Journal of the American Statistical Association"},{"key":"S026646661500033X_ref12","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1111\/j.2517-6161.1985.tb01335.x","article-title":"Locally best invariant tests of the error covariance matrix of the linear regression model","volume":"47","author":"King","year":"1985","journal-title":"Journal of the Royal Statistical Society. 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