  An ensemble of inspiraling supermassive black hole binaries should produce a
stochastic background of very low frequency gravitational waves. This
stochastic background is predicted to be a power law, with a spectral index of
-2/3, and it should be detectable by a network of precisely timed millisecond
pulsars, widely distributed on the sky. This paper reports a new "time slicing"
analysis of the 11-year data release from the North American Nanohertz
Observatory for Gravitational Waves (NANOGrav) using 34 millisecond pulsars.
Methods to flag potential "false positive" signatures are developed, including
techniques to identify responsible pulsars. Mitigation strategies are then
presented. We demonstrate how an incorrect noise model can lead to spurious
signals, and show how independently modeling noise across 30 Fourier
components, spanning NANOGrav's frequency range, effectively diagnoses and
absorbs the excess power in gravitational-wave searches. This results in a
nominal, and expected, progression of our gravitational-wave statistics.
Additionally we show that the first interstellar medium event in PSR J1713+0747
pollutes the common red noise process with low-spectral index noise, and use a
tailored noise model to remove these effects.
