Fully modified estimation in cointegrating polynomial regressions : extensions and Monte Carlo comparison

We study a set of fully modified (FM) estimators in multivariate cointegrating polynomial regressions. Such regressions allow for deterministic trends, stochastic trends, and integer powers of stochastic trends to enter the cointegrating relations. A new feasible generalized least squares estimator is proposed. Our estimator incorporates: (1) the inverse autocovariance matrix of multidimensional errors and (2) second-order bias corrections. The resulting estimator has the intuitive interpretation of applying a weighted least squares objective function to filtered data series. Moreover, the required second-order bias corrections are convenient byproducts of our approach and lead to a conventional asymptotic inference. Based on different FM estimators, multiple multivariate KPSS-type of tests for the null of cointegration are constructed. We then undertake a comprehensive Monte Carlo study to compare the performance of the FM estimators and the related tests. We find good performance of the proposed estimator and the implied test statistics for linear hypotheses and cointegration.