This paper first studies the full rank least squares estimator (FLSE) of the heavy-tailed vector error correction models. It is shown that the rate of convergence of the FLSE 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 when the tail index $\alpha\in (0,2)$. Furthermore, we show that the rate of convergence of the FLSE related to the short-term parameters is $n^{1/\alpha} tilde{L}(n)$ and its limiting distribution is a functional of two stable processes when $\alpha\in (1,2)$. However, when $\alpha\in (0,1)$, we show that the rate of convergence of the FLSE related to the short-term parameters is $n$ and its limiting distribution not only depends on the stationary component itself but also depends on the unit root component. Based on the FLSE, we then studied the limiting behavior of the reduced rank LSE (RLSE). The results related to the short-term parameters of both FLSE and RLSE are significantly different from those of heavy-tailed time series in the literature, and it may provide new insights in the area for future research. Simulation study is carried out to demonstrate the performance of both estimators. A real example with application to 3-month Treasury Bill rate, 1-year Treasury Bill and Federal Fund rate is given.

(This is a join work with She Rui in HKUST)