Abstract:
We prove that $m$ principal singular vectors of a matrix $X_{d}$
constructed on the basis of a time series, contained periodical
deterministic components with additive white noise, have equal
pseudo-spectra and their pseudo-spectral structure is identical to
that of the time series. The structures of pseudo-spectra of the
rest singular vectors differ from the structures of pseudo-spectra
of the principal vectors and the time series. It is shown that the
time series allow one to increase the resolving capacity and to
improve the statistical stability of spectral estimation.
