  We analyze timing noise from five years of Arecibo and Green Bank
observations of the seventeen millisecond pulsars of the North-American
Nanohertz Observatory for Gravitational Waves (NANOGrav) pulsar timing array.
The weighted autocovariance of the timing residuals was computed for each
pulsar and compared against two possible models for the underlying noise
process. The first model includes red noise and predicts the autocovariance to
be a decaying exponential as a function of time lag. The second model is
Gaussian white noise whose autocovariance would be a delta function. We also
perform a ``nearest-neighbor" correlation analysis. We find that the
exponential process does not accurately describe the data. Two pulsars,
J1643-1224 and J1910+1256, exhibit weak red noise, but the rest are well
described as white noise. The overall lack of evidence for red noise implies
that sensitivity to a (red) gravitational wave background signal is limited by
statistical rather than systematic uncertainty. In all pulsars, the ratio of
non-white noise to white noise is low, so that we can increase the cadence or
integration times of our observations and still expect the root-mean-square of
timing residual averages to decrease by the square-root of observation time,
which is key to improving the sensitivity of the pulsar timing array.
