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Cointegration analysis was developed for non-stationary linear processes thatexhibit stationary relationships between coordinates. Estimation of thecointegration relationships in a multi-dimensional cointegrated processtypically proceeds in two steps. First the rank is estimated, then thecointegration matrix is estimated, conditionally on the estimated rank (reducedrank regression). The asymptotics of the estimator is usually derived under theassumption of knowing the true rank. In this paper, we quantify the asymptoticbias and find the asymptotic distributions of the cointegration estimator incase of misspecified rank. Furthermore, we suggest a new class of weightedreduced rank estimators that allow for more flexibility in settings where rankselection is hard. We show empirically that a proper choice of weights can leadto increased predictive performance when there is rank uncertainty. Finally, weillustrate the estimators on empirical EEG data from a psychological experimenton visual processing.

Weighted Reduced Rank Estimators Under Cointegration Rank Uncertainty