Weighted reduced rank estimators under cointegration rank uncertainty

Cointegration analysis was developed for nonstationary linear processes that exhibit stationary relationships between coordinates. Estimation of the cointegration relationships in a multidimensional cointegrated process typically proceeds in two steps. First, the rank is estimated, then the auto-regression matrix is estimated, conditionally on the estimated rank (reduced rank regression). The asymptotics of the estimator is usually derived under the assumption of knowing the true rank. In this paper, we quantify the asymptotic bias and find the asymptotic distributions of the cointegration estimator in case of misspecified rank. Furthermore, we suggest a new class of weighted reduced rank estimators that allow for more flexibility in settings where rank selection is hard. We show empirically that a proper choice of weights can lead to increased predictive performance when there is rank uncertainty. Finally, we illustrate the estimators on empirical EEG data from a psychological experiment on visual processing.