Iterative Maximum Likelihood Estimation of Cointegrating Vectors1

This paper introduces an iterative method to estimate the cointegrating vectors in the error correction models. The method provides the asymptotically efficient estimators for the cointegrating vectors if iterated once or more. If it is iterated until convergence, we may obtain the maximum likelihood estimator by Johansen. For all values of 1 ≤ k ≤ ∞, the k-step iterative estimators are asymptotically equivalent, and as efficient as the maximum likelihood estimator. Their finite sample performances are, however, quite different for different values of k, most notably for the two extreme cases k = 1 and k = ∞. The finite-step iterative estimators generally perform better in small samples than the infinite-step iterative estimator, i.e., the maximum likelihood estimator. In particular, the former are much more robust than the latter, which is known to occasionally yield some extreme outliers in samples of relatively small size. Our iterative procedure indeed can be very useful in detecting the occurrences of outliers for the maximum likelihood estimator, since its realized values tend to deviate largely from those of the finite-step iterative estimators when the extreme outliers are produced. The proposed method is very flexible and can be easily implemented for the cointegrated models that are specified in an arbitrary structural form. First Draft: December 2003 This Version: January 2005