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Statistica Sinica 32 (2022), 2171-2198


Feifei Guo, Shiqing Ling and Zichuan Mi

Beijing Institute of Technology, Hong Kong University of Science and Technology
and Shanxi University of Finance and Economics

Abstract: This paper proposes an automated approach that uses adaptive shrinkage techniques to determine the cointegrating rank and estimate the parameters simultaneously in a vector error correction model with unknown order p when its noise is represented by independent and identically distributed heavy-tailed random vectors with tail index α ∈ (0, 2). We show that the estimated cointegrating rank and order p are equal to the true rank and the true order p0, respectively, with probability trending to one as the sample size n → ∞. The other estimated parameters achieve the oracle property. That is, they have the same rate of convergence and the same limiting distribution as those of the estimated parameters when the cointegrating rank and the true order p0 are known. This paper also proposes a data-driven procedure for selecting the tuning parameters. Simulation studies are carried out to evaluate the performance of the proposed procedure for finite samples. Lastly, we use our techniques to explore the long-run and short-run behavior of the prices of wheat, corn, and wheat flour in the United States.

Key words and phrases: Cointegration, heavy-tailed, LASSO, reduced rank LSE.

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