  This article addresses the measurement of the power spectrum of red noise
processes at the lowest frequencies, where the minimum acquisition time is so
long that it is impossible to average on a sequence of data record. Therefore,
averaging is possible only on simultaneous observation of multiple instruments.
This is the case of radio astronomy, which we take as the paradigm, but
examples may be found in other fields such as climatology and geodesy. We
compare the Bayesian confidence interval of the red-noise parameter using two
estimators, the spectrum average and the cross-spectrum. While the spectrum
average is widely used, the cross-spectrum using multiple instruments is rather
uncommon. With two instruments, the cross-spectrum estimator leads to the
Variance-Gamma distribution. A generalization to $q$ devices is provided, with
the example of the observation of millisecond pulsars with 5 radio telescopes.
