In this paper we propose an alternative characterization of
the central notion of cointegration, exploiting the relationship
between the autocovariance and the cross-covariance functions
of the series. This characterization leads us to propose a new
estimator of the cointegrating parameter based on the instrumental
variables (IV) methodology. The instrument is a delayed regressor
obtained from the 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, in
the I(1) case, with a semiparametric correction simpler
than the one required for the fully modified ordinary least squares
(FM-OLS), our fully modified instrumental variables (FM-IV) estimator
is median-unbiased, a mixture of normals, and asymptotically efficient.
As a consequence, standard inference can be conducted with this new
FM-IV estimator of the cointegrating parameter. We show by the use of
Monte Carlo simulations that the small sample gains with the new IV
estimator over OLS are remarkable.