ROBUST NONSTATIONARY REGRESSION by

This paper provides a robust statistical approach to nonstationary time series regression and inference. Fully modified extensions of traditional robust statistical procedures are developed that allow for endogeneities in the nonstation-ary regressors and serial dependence in the shocks that drive the regressors and the errors that appear in the equation being estimated. The suggested estima-tors involve semiparametric corrections to accommodate these possibilities, and they belong to the same family as the fully modified least-squares (FM-OLS) is not always smooth, and this paper develops generalized function methods to cope with this difficulty in the asymptot-ics. The results given here include a strong law of large numbers and some weak convergence theory for partial sums of generalized functions of random variables. The limit distribution theory for FM-LAD and FM-M estimators that is developed includes the case of finite variance errors and the case of heavy-tailed (infinite variance) errors. Some simulations and a brief empirical illustration are reported.