It is well known that the discrete Fourier transforms (DFTs) of a second order stationary time series between two distinct Fourier frequencies are asymptotically uncorrelated. In contrast for a large class of second order nonstationary time series, including locally stationary time series, this...

Motivated by a recent paper of Caiado et al. (2009), we investigate testing problems for spectral densities of time series with unequal sample sizes. We thereby focus on analyzing their mathematical properties and illustrate our results in a small simulation study.

The paper reconsiders the autoregressive aided periodogram bootstrap (AAPB) which has been suggested in Kreiss and Paparoditis (2003) [18]. Their idea was to combine a time domain parametric and a frequency domain nonparametric bootstrap to mimic not only a part but as much as possible the...