First Stage Estimation of Fractional Cointegration

In a fractionally cointegrated model, we analyze, both theoretically and by means of a Monte Carlo experiment, the performance of the most popular first stage estimation methods, including ordinary and narrow band least squares (Robinson, 1994), difference taper narrow band least squares (Chen and Hurvich, 2003a), instrumental variables (Robinson and Gerolimetto, 2006), and compare it with the behavior of a new proposal, the integrated ordinary least squares. An appropriate version of this latter estimator (and also of the instrumental variables one) achieves in all circumstances the fastest convergence rate (among other first stage methods) and performs well in finite samples. The use of improved first stage methods is most important in cases of low collective memory of regressor and cointegrating error. This is particularly relevant in multivariate settings, where the key parameters which rule the convergence properties of the estimators are the memories of adjacent cointegrating subspaces.