This is the abstract of a paper that appeared in the International Journal of Remote Sensing. It has been sitting around for a while, but I think that its points are still valid.
Many researchers are interested in the dynamics of the
atmosphere and are looking for possible wavelike phenomena in the
atmosphere to explain the distribution of clouds and rain. However,
some of them have been using mathematically faulty methods to look
for these waves. There are many reports of waves with periods between
30 and 60 days, sometimes called intraseasonal oscillations,
that seem to be based on the notion procedure: take a random time
series; filter it with a bandpass filter; plot the result; and claim
that the resulting oscillating time series is evidence of
oscillations in the atmosphere. This was first done by Madden and
Julian (1971, 1972, in Journal of the Atmospheric Sciences).
We should realize that this procedure will always produce
oscillations at the center frequency of the bandpass filter,
regardless of the nature of the random process being investigated. No
valid conclusion about the presence or absence of waves can be drawn
from this procedure. This has not been generally recognized.
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Andrew S. Milman,
amilman@ieee.org. Last Modified 04/06/06.