| Abstract: | We introduce a multivariate Lagrange multiplier (LM) test forfractional integration. We derive and analyze the LM statisticand show that it is asymptotically noncentral chi-squared distributedunder local alternatives, and that, under Gaussianity, the LMtest is asymptotically efficient against local alternatives.It is shown that the regression variant in Breitung and Hassler(2002, Journal of Econometrics 110, 167–185) is not equivalentto the LM test in the multivariate case, although it is in theunivariate case. A generalization of the LM test that explicitlyallows for different integration orders for each variable isalso introduced. The finite sample properties of the LM testare evaluated by Monte Carlo experiments which demonstrate thatit is superior to the Breitung and Hassler (2002) test. An applicationto multivariate time series of real interest rates for six countriesis offered, demonstrating that more clear-cut evidence can bedrawn from multivariate tests compared to conducting severalunivariate tests. |
