  The advent of time domain astronomy is revolutionizing our understanding of
the Universe. Programs such as the Catalina Real-time Transient Survey (CRTS)
or the Palomar Transient Factory (PTF) surveyed millions of objects for several
years, allowing variability studies on large statistical samples. The
inspection of $\approx$250k quasars in CRTS resulted in a catalogue of 111
potentially periodic sources, put forward as supermassive black hole binary
(SMBHB) candidates. A similar investigation on PTF data yielded 33 candidates
from a sample of $\approx$35k quasars. Working under the SMBHB hypothesis, we
compute the implied SMBHB merger rate and we use it to construct the expected
gravitational wave background (GWB) at nano-Hz frequencies, probed by pulsar
timing arrays (PTAs). After correcting for incompleteness and assuming virial
mass estimates, we find that the GWB implied by the CRTS sample exceeds the
current most stringent PTA upper limits by almost an order of magnitude. After
further correcting for the implicit bias in virial mass measurements, the
implied GWB drops significantly but is still in tension with the most stringent
PTA upper limits. Similar results hold for the PTF sample. Bayesian model
selection shows that the null hypothesis (whereby the candidates are false
positives) is preferred over the binary hypothesis at about $2.3\sigma$ and
$3.6\sigma$ for the CRTS and PTF samples respectively. Although not decisive,
our analysis highlights the potential of PTAs as astrophysical probes of
individual SMBHB candidates and indicates that the CRTS and PTF samples are
likely contaminated by several false positives.
