Reduced rank regression in cointegrated models

The coefficient matrix of a cointegrated first-order autoregression is estimated by reduced rank regression (RRR), depending on the larger canonical correlations and vectors of the first difference of the observed series and the lagged variables. In a suitable coordinate system the components of the least-squares (LS) estimator associated with the lagged nonstationary variables are of order 1/T, where T is the sample size, and are asymptotically functionals of a Brownian motion process; the components associated with the lagged stationary variables are of the order T−1/2 and are asymptotically normal. The components of the RRR estimator associated with the stationary part are asymptotically the same as for the LS estimator. Some components of the RRR estimator associated with nonstationary regressors have zero error to order 1/T and the other components have a more concentrated distribution than the corresponding components of the LS estimator.