Inference for the VEC(1) model with a heavy-tailed linear process errors*
研究了噪声为重尾线性过程的VEC(1)模型，发现长期参数的最小二乘估计收敛速度为n且极限分布为随机积分，短期参数估计不一致，并提出了自适应收缩方法确定协整秩。
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 α∈(0,2). 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 r0 can be consistently selected despite the fact that the LSE related to the short-term parameters is not consistently estimable when the tail index α∈(1,2). 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.