  Noise is ubiquitous in pulsar signals where red noise has been attributed to
effects arising from the interstellar medium, spin noise, and pulsar mode
changes, among others. The red noise, however, has not been detected in all
pulsars. Using the dataset from the North American Nanohertz Observatory for
Gravitational Waves (NANOGrav), we investigate twenty-three pulsars and show
that an evaluation of the mean square deviation and probability distribution of
timing residuals can provide a straightforward way of determining the presence
of red noise. The results agree with those reported in the literature. The
model-free method presented could complement the normally more sophisticated
model-dependent way of determining red noise in timing residuals.
