"Test for cointegration rank in general vector autoregressions"
Bent Nielsen
Dept of Economics and Nuffield College, Oxford University, Oxford
Abstract
Johansen derived the asymptotic theory for his cointegration rank test statisic for
a vector autoregression where the parameters are restricted so the process is integrated
of order one. It is investigated to what extent these parameter restrictions
are binding. The eigenvalues of Johansen’s eigenvalue problem are shown to have the
same consistency rates accross the parameter space. The test statistic is shown to
have the usual asymptotic distribution as long as the possibilities of additional unit
roots and of singular explosiveness are ruled out. To prove the results the convergence
of stochastic integrals with respect to singular explosive processes is considered.