Resumen de Distribution-free Tests of Fractional Cointegration

Carlos Velasco, Javier Hualde Bilbao

• 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 GLS-type of corrections which 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 which 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 analysed by means of a Monte Carlo experiment.