Abstract :
We propose tests of the null of spurious relationship against the alternative of
fractional cointegration among the components of a vector of fractionally integrated
time series+ Our test statistics have an asymptotic chi-square distribution
under the null and rely on generalized least squares–type of corrections that control
for the short-run correlation of the weak dependent components of the fractionally
integrated processes+ We emphasize corrections based on nonparametric
modelization of the innovations’ autocorrelation, relaxing important conditions
that are standard in the literature and, in particular, being able to consider simultaneously
~asymptotically! stationary or nonstationary processes+ Relatively weak
conditions on the corresponding short-run and memory parameter estimates are
assumed+ The new tests are consistent with a divergence rate that, in most of the
cases, as we show in a simple situation, depends on the cointegration degree+
Finite-sample properties of the tests are analyzed by means of a Monte Carlo
experiment+
