& Magnus, J.R. (2000). On the sensitivity of the usual t- and F-tests to covariance misspecification. Journal of Econometrics 95
Author(s) from Durham
We consider the standard linear regression model with all standard assumptions, except that the disturbances are not white noise, but distributed Full-size image (<1 K) where Full-size image (<1 K). Our interest lies in testing linear restrictions using the usual F-statistic based on OLS residuals. We are not interested in finding out whether θ=0 or not. Instead we want to find out what the effect is of possibly nonzero θ on the F-statistic itself. We propose a sensitivity statistic φ 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 misspecification when θ is close to zero. Some finite and asymptotic properties of ϕ are studied, as well as its behaviour in the special case of an AR(1) process near the unit root.