M-Estimations for Regressions with Integrated Regressors and Arma Errors

General M-estimation is developed for regression models with integrated regressors and autoregressive moving average (ARMA) errors, in which the ARMA parameters are jointly estimated with the regression parameters. The large sample distribution of the M-estimator is derived. Allowing the regressors to be dependent on the error terms, a parametric 'fully modified' (FM) M-estimator is proposed. In cases of ARMA errors, a Monte-Carlo experiment reveals superiority of the parametric estimators over the semiparametric FM M-estimator of Phillips Econometric Theory 11 (1995, p 912) in terms of empirical mean squared error