  Pulsar timing arrays (PTAs) are designed to detect low-frequency
gravitational waves (GWs). GWs induce achromatic signals in PTA data, meaning
that the timing delays do not depend on radio-frequency. However, pulse arrival
times are also affected by radio-frequency dependent "chromatic" noise from
sources such as dispersion measure (DM) and scattering delay variations.
Furthermore, the characterization of GW signals may be influenced by the choice
of chromatic noise model for each pulsar. To better understand this effect, we
assess if and how different chromatic noise models affect achromatic noise
properties in each pulsar. The models we compare include existing DM models
used by NANOGrav and noise models used for the European PTA Data Release 2
(EPTA DR2). We perform this comparison using a subsample of six pulsars from
the NANOGrav 15 yr data set, selecting the same six pulsars as from the EPTA
DR2 six-pulsar dataset. We find that the choice of chromatic noise model
noticeably affects the achromatic noise properties of several pulsars. This is
most dramatic for PSR J1713+0747, where the amplitude of its achromatic red
noise lowers from $\log_{10}A_{\text{RN}} = -14.1^{+0.1}_{-0.1}$ to
$-14.7^{+0.3}_{-0.5}$, and the spectral index broadens from $\gamma_{\text{RN}}
= 2.6^{+0.5}_{-0.4}$ to $\gamma_{\text{RN}} = 3.5^{+1.2}_{-0.9}$. We also
compare each pulsar's noise properties with those inferred from the EPTA DR2,
using the same models. From the discrepancies, we identify potential areas
where the noise models could be improved. These results highlight the potential
for custom chromatic noise models to improve PTA sensitivity to GWs.
