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The main purpose of this paper is to show that, contrary to what is generally believed, omnibus specification tests only have substantial local power against alternatives in a finite-dimensional space (usually unknown to the researcher). We call such a space the<jats:italic>principal space<\/jats:italic>. We characterize and estimate the principal space for Cram\u00e9r\u2013von Mises tests. These results are some of the by-products of a detailed theoretical power analysis carried out in the paper. This investigation focuses on the class of the so-called integrated consistent tests under possibly heteroskedastic time series. A Monte Carlo experiment examines the finite-sample properties of tests and estimators of preferred alternatives. Finally, an application of our theory to test the martingale difference hypothesis of some exchange rates provides new information on the rejection of omnibus tests and illustrates our findings.<\/jats:p>","DOI":"10.1017\/s0266466608090051","type":"journal-article","created":{"date-parts":[[2009,1,9]],"date-time":"2009-01-09T14:13:57Z","timestamp":1231510437000},"page":"162-194","source":"Crossref","is-referenced-by-count":51,"title":["ON THE LACK OF POWER OF OMNIBUS SPECIFICATION TESTS"],"prefix":"10.1017","volume":"25","author":[{"given":"J. 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