INSTRUMENTAL VARIABLE INTERPRETATION OF COINTEGRATION WITH INFERENCE RESULTS FOR FRACTIONAL COINTEGRATION
提出协整的新刻画，基于自协方差与互协方差关系，构建工具变量估计量，证明其一致性和渐近分布，在I(1)情形下FM-IV估计量中位数无偏且渐近有效，蒙特卡洛模拟显示小样本下优于OLS。
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.