Co-integration rank test with multiple changes in volatility

Abstract

Co-integration rank test by Johansen (1988, 1991) and Johansen and Juselius (1990) presumes error terms characterized by i.i.d Gaussian process. However, a wide range of studies providing evidence for poor finite sample size and power properties under heteroskedastic innovation. Cavaliere et al. (2010a, 2010b, 2014) proposing a wild bootstrap implementation of the conventional Johansen test. These studies introduce a framework for co-integrated relationships, allowing conditional and unconditional heteroskedasticity, including single and multiple volatility breaks in the covariance matrix. The bootstrap test performs very well generally, especially when compared to the standard Johansen test. We compare the conventional Johansen test and it's wild bootstrap implementation via Monte-Carlo simulation. The effects of single and multiple volatility breaks are examined in detail. The consequence of slow adjustment speed in co-integrated relationship assessed as well. Our findings suggest highly unreliable rank estimation with both tests subject to certain conditions.