On determination of cointegration ranks

We propose a new method to determine the cointegration rank in the error correction model of Engle and Granger (1987). To this end, we first estimate the cointegration vectors in terms of a residual-based principal component analysis. Then the cointegration rank, together with the lag order, is determined by a penalized goodness-of-fit measure. We have shown that the estimated cointegration vectors are asymptotically normal, and our estimation for the cointegration rank is consistent. Our approach is more robust than the conventional likelihood based methods, as we do not impose any assumption on the form of the error distribution in the model, and furthermore we allow the serial dependence in the error sequence. The proposed methodology is illustrated with both simulated and real data examples. The advantage of the new method is particularly pronounced in the simulation with non-Gaussian and/or serially dependent errors.