Fully modified least squares estimation and inference for systems of cointegrating polynomial regressions

We consider fully modified least squares estimation for systems of cointegrating polynomial regressions, i. e., systems of regressions that include deterministic variables, integrated processes and their powers as regressors. The errors are allowed to be correlated across equations, over time and with the regressors. Whilst, of course, fully modified OLS and GLS estimation coincide - for any regular weighting matrix - without restrictions on the parameters and with the same regressors in all equations, this equivalence breaks down, in general, in case of parameter restrictions and/or different regressors across equations. Consequently, we discuss in detail restricted fully modified GLS estimators and inference based upon them.