Abstract :
We analyze the properties of the conventional Gaussian-based cointegrating rank
tests of Johansen (1996, Likelihood-Based Inference in Cointegrated Vector Autoregressive
Models) in the case where the vector of series under test is driven
by globally stationary, conditionally heteroskedastic (martingale difference) innovations.
We first demonstrate that the limiting null distributions of the rank statistics
coincide with those derived by previous authors who assume either independent and
identically distributed (i.i.d.) or (strict and covariance) stationary martingale difference
innovations.We then propose wild bootstrap implementations of the cointegrating
rank tests and demonstrate that the associated bootstrap rank statistics replicate
the first-order asymptotic null distributions of the rank statistics. We show that the
same is also true of the corresponding rank tests based on the i.i.d. bootstrap of
Swensen (2006, Econometrica 74, 1699–1714). The wild bootstrap, however, has
the important property that, unlike the i.i.d. bootstrap, it preserves in the resampled
data the pattern of heteroskedasticity present in the original shocks. Consistent with
this, numerical evidence suggests that, relative to tests based on the asymptotic critical
values or the i.i.d. bootstrap, the wild bootstrap rank tests perform very well in
small samples under a variety of conditionally heteroskedastic innovation processes.
An empirical application to the term structure of interest rates is given.
