A fractional multivariate long memory model for the US and the Canadian real output

This paper uses an extension of the univariate tests of Robinson [J. Am. Stat. Assoc. 89 (1994) 1420] to the multivariate case. We examine the degrees of integration of the real output in the US and Canada throughout a bivariate system. The results show that if the disturbances are white noise, the null hypothesis of two unit roots is rejected in favour of higher orders of integration. However, if a VAR(1) structure is assumed, the unit root null cannot be rejected. Thus, both series are clearly nonstationary in spite of the cross-correlation permitted across countries.