S-Estimation in the Linear Regression Model with Long-Memory Error Terms

The phenomenon of long-memory plays an important role in economics. This paper considers the asymptotic properties of S -estimators -- a class of robust estimates with a high breakdown-point and good asymptotic properties -- in the linear regression model with long memory error terms. Here we assume mild regularity conditions on the regressors, which are sufficiently weak to cover, for example, polynomial trends and i.i.d. carries. It turns out that S -estimators are asymptotically normal with a variance-covariance structure which, in the case of long memory, is similar to the structure in the i.i.d. case. In this case S -estimators also have the same rate of convergence as the least squares estimator and the BLUE. It is possible to extend these results to a class of robust estimators which have high breakdown and high efficiency simultaneously, so-called MM-estimators. But MM-estimators are difficult to compute in practice.