  The nanohertz gravitational wave background (GWB) is expected to be an
aggregate signal of an ensemble of gravitational waves emitted predominantly by
a large population of coalescing supermassive black hole binaries in the
centres of merging galaxies. Pulsar timing arrays, ensembles of extremely
stable pulsars, are the most precise experiments capable of detecting this
background. However, the subtle imprints that the GWB induces on pulsar timing
data are obscured by many sources of noise. These must be carefully
characterized to increase the sensitivity to the GWB. In this paper, we present
a novel technique to estimate the optimal number of frequency coefficients for
modelling achromatic and chromatic noise and perform model selection. We also
incorporate a new model to fit for scattering variations in the pulsar timing
package temponest and created realistic simulations of the European Pulsar
Timing Array (EPTA) datasets that allowed us to test the efficacy of our noise
modelling algorithms. We present an in-depth analysis of the noise properties
of 25 millisecond pulsars (MSPs) that form the second data release (DR2) of the
EPTA and investigate the effect of incorporating low-frequency data from the
Indian PTA collaboration. We use enterprise and temponest packages to compare
noise models with those reported with the EPTA DR1. We find that, while in some
pulsars we can successfully disentangle chromatic from achromatic noise owing
to the wider frequency coverage in DR2, in others the noise models evolve in a
more complicated way. We also find evidence of long-term scattering variations
in PSR J1600$-$3053. Through our simulations, we identify intrinsic biases in
our current noise analysis techniques and discuss their effect on GWB searches.
The results presented here directly help improve sensitivity to the GWB and are
already being used as part of global PTA efforts.
