ROBUST NONSTATIONARY REGRESSION

This paper provides a robust statistical approach to nonstationary tim e series regression and inference. Fully modified extensions of tradit ional robust statistical procedures are developed that allow for endog eneities in the nonstationary regressors and serial dependence in the shocks that drive the regressors and the errors that appear in the equ ation being estimated. The suggested estimators involve semiparametric corrections to accommodate these possibilities, and they belong to th e same family as the fully modified least-squares (FM-OLS) estimator o f Phillips and Hansen (1990, Review of Economic Studies 57, 99-125). S pecific attention is given to fully modified least absolute deviation (FM-LAD) estimation and fully modified M (FM-M) estimation. The criter ion function for LAD and some M-estimators is not always smooth, and t his paper develops generalized function methods to cope with this diff iculty in the asymptotics. 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 the ory for FM-LAD and FM-M estimators that is developed includes the case of finite variance errors and the case of heavy-tailed (infinite vari ance) errors. Some simulations and a brief empirical illustration are reported.