  In this paper we propose a nonparametric procedure for validating the
assumption of stationarity in multivariate locally stationary time series
models. We develop a bootstrap assisted test based on a Kolmogorov-Smirnov type
statistic, which tracks the deviation of the time varying spectral density from
its best stationary approximation. In contrast to all other nonparametric
approaches, which have been proposed in the literature so far, the test
statistic does not depend on any regularization parameters like smoothing
bandwidths or a window length, which is usually required in a segmentation of
the data. We additionally show how our new procedure can be used to identify
the components where non-stationarities occur and indicate possible extensions
of this innovative approach. We conclude with an extensive simulation study,
which shows finite sample properties of the new method and contains a
comparison with existing approaches.
