Exploiting Infinite Variance through Dummy Variables in an AR model

In this paper we consider estimation and unit root testing in AR(1) models with infinite variance innovations. Specifically, we study the asymptotic properties of estimators obtained by dummying out ”large” innovations, i.e. exceeding a given threshold. These estimators reflect the common practice of dealing with large residuals by including impulse dummies in the estimated regression. Iterative versions of the dummy-variable estimator are also discussed. We provide conditions on the threshold and on the preliminary parameter estimator which ensure that (i) the dummy-based estimator is consistent at higher rates than the basic OLS estimator, and (ii) an asymptotically normal test statistic for the unit root hypothesis can be derived. Our results are related to those obtained for a class of M-estimators in Knight (1989) where, however, their existence and computability is not discussed. Also, due to its non-smoothness, the dummy-variable estimator does not fall within the class of estimators considered in Knight (1989).