A new instrumental variable approach for estimation and testing in fractional cointegrating regressions

In this paper we propose an alternative characterization of the central notion of cointegration, exploiting the relationship between the autocorrelation and the crosscorrelation functions of the series. This characterization lead us to propose a new estimator of the co integrating parameter based on the instrumental variables methodology. The instrument is a delayed replica of the regressor variable in a conditional bivariate system of nonstationary fractionally integrated processes with a weakly stationary error correction term. We prove the consistency of this estimator and derive its limiting distribution. We also show that with a semi-parametric correction the estimator for the unit root case is median-unbiased, a mixture of normals and asymptotically efficient. As a consequence, standard inference can be conducted with this fully modified instrumental variable estimator of the co integrating parameter.