  We carried out a new and sensitive search for long-period variability in the
prototype of the Mira class of long-period pulsating variables, o Ceti (Mira
A), the closest and brightest Mira variable. We conducted this search using an
unbroken light curve from 1902 to the present, assembled from the visual data
archives of five major variable star observing organizations from around the
world. We applied several time-series analysis techniques to search for two
specific kinds of variability: long secondary periods (LSPs) longer than the
dominant pulsation period of ~333 days, and long-term period variation in the
dominant pulsation period itself. The data quality is sufficient to detect
coherent periodic variations with photometric amplitudes of 0.05 mag or less.
We do not find evidence for coherent LSPs in o Ceti to a limit of 0.1 mag,
where the amplitude limit is set by intrinsic, stochastic, low-frequency
variability of approximately 0.1 mag. We marginally detect a slight modulation
of the pulsation period similar in timescale to that observed in the Miras with
meandering periods, but with a much lower period amplitude of +/-2 days.
However, we do find clear evidence of a low-frequency power-law component in
the Fourier spectrum of o Ceti's long-term light curve. The amplitude of this
stochastic variability is approximately 0.1 mag at a period of 1000 days, and
it exhibits a turnover for periods longer than this. This spectrum is similar
to the red noise spectra observed in red supergiants.
