Does a 'stochastic' background of gravitational waves exist in the
  pulsar timing band?
  We investigate the effects of gravitational waves (GWs) from a simulated
population of binary super-massive black holes (SMBHs) on pulsar timing array
datasets. We construct a distribution describing the binary SMBH population
from an existing semi-analytic galaxy formation model. Using realizations of
the binary SMBH population generated from this distribution, we simulate pulsar
timing datasets with GW-induced variations. We find that the statistics of
these variations do not correspond to an isotropic, stochastic GW background.
The "Hellings & Downs" correlations between simulated datasets for different
pulsars are recovered on average, though the scatter of the correlation
estimates is greater than expected for an isotropic, stochastic GW background.
These results are attributable to the fact that just a few GW sources dominate
the GW-induced variations in every Fourier frequency bin of a 5-year dataset.
Current constraints on the amplitude of the GW signal from binary SMBHs will be
biased. Individual binary systems are likely to be detectable in 5-year pulsar
timing array datasets where the noise is dominated by GW-induced variations.
Searches for GWs in pulsar timing array data therefore need to account for the
effects of individual sources of GWs.
