  For many relevant statistics of multivariate time series, no valid frequency
domain bootstrap procedures exist. This is mainly due to the fact that the
distribution of such statistics depends on the fourth-order moment structure of
the underlying process in nearly every scenario, except for some special cases
like Gaussian time series. In contrast to the univariate case, even additional
structural assumptions such as linearity of the multivariate process or a
standardization of the statistic of interest do not solve the problem. This
paper focuses on integrated periodogram statistics as well as functions thereof
and presents a new frequency domain bootstrap procedure for multivariate time
series, the multivariate frequency domain hybrid bootstrap (MFHB), to fill this
gap. Asymptotic validity of the MFHB procedure is established for general
classes of periodogram-based statistics and for stationary multivariate
processes satisfying rather weak dependence conditions. A simulation study is
carried out which compares the finite sample performance of the MFHB with that
of the moving block bootstrap.
