On the sensitivity of the usual t- and F-tests to covariance misspeci"cation
نویسندگان
چکیده
We consider the standard linear regression model with all standard assumptions, except that the disturbances are not white noise, but distributed N(0,p2X(h)) where X(0)"I n . Our interest lies in testing linear restrictions using the usual F-statistic based on OLS residuals. We are not interested in "nding out whether h"0 or not. Instead we want to "nd out what the e!ect is of possibly nonzero h on the F-statistic itself. We propose a sensitivity statistic / for this purpose, discuss its distribution, and obtain a practical and easy-to-use decision rule to decide whether the F-test is sensitive or not to covariance misspeci"cation when h is close to zero. Some "nite and asymptotic properties of u are studied, as well as its behaviour in the special case of an AR(1) process near the unit root. ( 2000 Elsevier Science S.A. All rights reserved. JEL classixcation: C12; C22; C51; C52
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