Dette, HolgerHildebrandt, Thimo2010-05-032010-05-032010-05-03http://hdl.handle.net/2003/2713110.17877/DE290R-8593In a recent paper Eichler (2008) considered a class of non- and semiparametric hypotheses in multivariate stationary processes, which are characterized by a functional of the spectral density matrix. The corresponding statistics are obtained using kernel estimates for the spectral distribution and are asymptotically normal distributed under the null hypothesis and local alternatives. In this paper we derive the asymptotic properties of these test statistics under fixed alternatives. In particular we show also weak convergence but with a different rate compared to the null hypothesis.enDiscussion Paper / SFB 823;13/2010Goodness-of-fit testKernel estimateSmoothed periodogramStationary processWeak convergence under the alternative310330620report