DISTRIBUTION-FREE TESTS OF FRACTIONAL COINTEGRATION

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+