A Note on Mixed Stable Limit Theory for the OLSE and the Robustness of Subsampling Wald Tests

We are occupied with a simple example concerning the limit theory of the OLSE when the innovation process of the regression has the form of a martingale transform the i.i.d. part of which lies in the domain of attraction of an \alpha-stable distribution, the scalling sequence has a potentially diverging truncated \alpha-moment and the regressor process is asymptotically stationary. We obtain rates that reflect the stability parameter as well as the slow variations present in the aforementioned sequences and mixtures of stable limits. We also derive asymptotic exactness, consistency as well as local asymptotic unbiaseness under appropriate local alternatives for relevant Wald tests derived by subsampling