Inference for the VEC(1) model with a heavy-tailed linear process errors*

This article studies the first-order vector error correction (VEC(1)) model when its noise is a linear process of independent and identically distributed (i.i.d.) heavy-tailed random vectors with a tail index (Formula presented.). We show that the rate of convergence of the least squares estimator (LSE) related to the long-run parameters is n (sample size) and its limiting distribution is a stochastic integral in terms of two stable random processes, while the LSE related to the short-term parameters is not consistent. We further propose an automated approach via adaptive shrinkage techniques to determine the cointegrating rank in the VEC(1) model. It is demonstrated that the cointegration rank r ₀ can be consistently selected despite the fact that the LSE related to the short-term parameters is not consistently estimable when the tail index (Formula presented.). Simulation studies are carried out to evaluate the performance of the proposed procedure in finite samples. Last, we use our techniques to explore the long-run and short-run behavior of the monthly prices of wheat, corn, and wheat flour in the United States.