  The North American Nanohertz Observatory for Gravitational Waves (NANOGrav)
has recently reported strong statistical evidence for a common-spectrum
red-noise process for all pulsars, as seen in their 12.5-yr analysis for an
isotropic stochastic gravitational-wave background. However, there is currently
very little evidence for quadrupolar spatial correlations across the pulsars in
the array, which is needed to make a confident claim of detection of a
stochastic background. Here we give a frequentist analysis of a very simple
signal+noise model showing that the current lack of evidence for spatial
correlations is consistent with the magnitude of the correlation coefficients
for pairs of Earth-pulsar baselines in the array, and the fact that pulsar
timing arraysbare most-likely operating in the intermediate-signal regime. We
derive analytic expressions that allow one to compare the expected values of
the signal-to-noise ratios for both the common-spectrum and cross-correlation
estimators.
