The comparison of two spectral density functions using the bootstrap
Journal of Statistical Computation and Simulation
Time series: theory and methods
Time series: theory and methods
Nonparametric approach for non-Gaussian vector stationary processes
Journal of Multivariate Analysis
Comparison tests for the spectra of dependent multivariate time series
Stochastic modelling in physical oceanography
Testing nonparametric and semiparametric hypotheses in vector stationary processes
Journal of Multivariate Analysis
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In a recent paper, Eichler (2008) [11] 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 normally 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 also show weak convergence but with a different rate compared to the null hypothesis. We also discuss potential statistical applications of the asymptotic theory by means of a small simulation study.