  Recent observations from several pulsar timing array (PTA) collaborations
have unveiled compelling evidence for a stochastic signal in the nanohertz
band. This signal aligns remarkably with a gravitational wave (GW) background,
potentially originating from the first-order color charge confinement phase
transition. Distinct quantum chromodynamics (QCD) matters, such as quarks or
gluons, and diverse phase transition processes thereof can yield disparate GW
energy density spectra. In this paper, employing the Bayesian analysis on the
NANOGrav 15-year data set, we explore the compatibility with the observed PTA
signal of the GW from phase transitions of various QCD matter scenarios in the
framework of the holographic QCD. We find that the PTA signal can be
effectively explained by the GW from the confinement-deconfinement phase
transition of pure quark systems in a hard wall model of the holographic QCD
where the bubble dynamics, one important source of the GWs, is of the Jouguet
detonations. Notably, our analysis decisively rules out the plausibility of the
pure gluon QCD-matter scenario and the non-runaway bubble dynamics model for
the phase transition in explaining the observed PTA signal.
