It is widely accepted that the Gaussian assumption is too restrictive to model either financial or some important macroeconomic variables, because their distributions exhibit asymmetry and heavy tails. In this paper we develop the asymptotic theory for econometric cointegration processes under the assumption of infinite variance innovations with different distributional tail behavior. We extend some of the results of Park and Phillips which were derived under the assumption of finite variance errors.
"Cointegrated processes with infinite variance innovations." Ann. Appl. Probab. 8 (3) 775 - 792, August 1998. https://doi.org/10.1214/aoap/1028903450