On the sensitivity of the usual t- and F-tests to covariance misspecification

摘要

We consider the standard linear regression model with all standard assumptions, except that the disturbances are not white noise, but distributed N (0, #delta#~2#OMEGA#(0)) where #OMEGA#(0) = I_n. Our interest lies in testing linear restrictions using the usual F-statistic based on OLS residuals. We are not interested in finding out whether #theta# =0 or not. Instead we want to find out what the effect is of possibly nonzero 0 on theF-statistic itself. We propose a sensitivity statistic #PHI# for this purpose, discuss its distribution, and obtain a practical and easy-to-use decision rule ot decie whether the F-test is sensitive or not to covariance misspecification when 0 is close to zero. Some finite and asymptotic properties of #psi# are studied, as well as its behaviour in the special case of an AR (1) process near the unit root.