  In this paper, we investigate the testing problem that the spectral density
matrices of several, not necessarily independent, stationary processes are
equal. Based on an $L_2$-type test statistic, we propose a new nonparametric
approach, where the critical values of the tests are calculated with the help
of randomization methods. We analyze asymptotic exactness and consistency of
these randomization tests and show in simulation studies that the new
procedures posses very good size and power characteristics.
