  Using Fourier and wavelet analysis, we critically re-assess the significance
of our detection of periodic pulsations in coronal loops. We show that the
proper identification of the frequency dependence and statistical properties of
the different components of the power spectra provies a strong argument against
the common practice of data detrending, which tends to produce spurious
detections around the cut-off frequency of the filter. In addition, the white
and red noise models built into the widely used wavelet code of Torrence &
Compo cannot, in most cases, adequately represent the power spectra of coronal
time series, thus also possibly causing false positives. Both effects suggest
that several reports of periodic phenomena should be re-examined. The Torrence
& Compo code nonetheless effectively computes rigorous confidence levels if
provided with pertinent models of mean power spectra, and we describe the
appropriate manner in which to call its core routines. We recall the meaning of
the default confidence levels output from the code, and we propose new
Monte-Carlo-derived levels that take into account the total number of degrees
of freedom in the wavelet spectra. These improvements allow us to confirm that
the power peaks that we detected have a very low probability of being caused by
noise.
