  We investigate timing and spectral characteristics of the transient X-ray
pulsar 2S 1417$-$624 during its 2018 outburst with \emph{NICER} follow up
observations. We describe the spectra with high-energy cut-off and partial
covering fraction absorption (PCFA) model and present flux-dependent spectral
changes of the source during the 2018 outburst. Utilizing the correlation-mode
switching of the spectral model parameters, we confirm the previously reported
sub-critical to critical regime transitions and we argue that secondary
transition from the gas-dominated to the radiation pressure-dominated disc do
not lead to significant spectral changes below 12 keV. Using the existing
accretion theories, we model the spin frequency evolution of 2S 1417$-$624 and
investigate the noise processes of a transient X-ray pulsar for the first time
using both polynomial and luminosity-dependent models for the spin frequency
evolution. For the first model, the power density spectrum of the torque
fluctuations indicate that the source exhibits red noise component ($\Gamma
\sim -2$) within the timescales of outburst duration which is typical for
disc-fed systems. On the other hand, the noise spectrum tends to be white on
longer timescales with high timing noise level that indicates an ongoing
accretion process in between outburst episodes. For the second model, most of
the red noise component is eliminated and the noise spectrum is found to be
consistent with a white noise structure observed in wind-fed systems.
