Statistics and Its Interface

Volume 2 (2009)

Number 1

On determination of cointegration ranks

Pages: 45 – 56



Qiaoling Li (School of Mathematical Sciences, Peking University, Beijing, China)

Jiazhu Pan (Department of Statistics & Modelling Science, University of Strathclyde, Glasgow, Scotland, United Kingdom)

Qiwei Yao (Department of Statistics, London School of Economics, London, United Kingdom)


We propose a new method to determine the cointegration rank in the error correction model (ECM). The cointegration rank, together with the lag order, is determined by a penalized goodness-of-fit measure. We show that the estimated cointegration vectors are consistent with a convergence rate $T$, where $T$ is the sample size, 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. 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.


cointegration, error correction models, penalized goodness-of-fit criteria, model selection

2010 Mathematics Subject Classification

Primary 62M10, 62P20. Secondary 62H12.

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