An algorithm is presented which generates pairs of oscillatory random time
series which have identical periodograms but differ in the number of
oscillations. This result indicate the intrinsic limitations of spectral
methods when it comes to the task of measuring frequencies. Other examples, one
from medicine and one from bifurcation theory, are given, which also exhibit
these limitations of spectral methods. For two methods of spectral estimation
it is verified that the particular way end points are treated, which is
specific to each method, is, for long enough time series, not relevant for the
main result.Comment: 18 pages, 6 figures (Referee did not like the previous title. Many
other changes
