  This paper deals with the comparison of several stationary processes with
unequal sample sizes. We provide a detailed theoretical framework on the
testing problem for equality of spectral densities in the bivariate case, after
which the generalization of our approach to the m dimensional case and to other
statistical applications (like testing for zero correlation or clustering of
time series data with different length) is straightforward. We prove asymptotic
normality of an appropriately standardized version of the test statistic both
under the null and the alternative and investigate the finite sample properties
of our method in a simulation study. Furthermore we apply our approach to
cluster financial time series data with different sample length.
