  We present a statistical analysis of the gravoturbulent velocity fluctuations
in molecular cloud complexes extracted from our "Cloud Factory" galactic-scale
ISM simulation suite. For this purpose, we produce non-LTE $^{12}$CO J=1-0
synthetic observations and apply the Principal Component Analysis (PCA)
reduction technique on a representative sample of cloud complexes. The velocity
fluctuations are self-consistently generated by different physical mechanisms
at play in our simulations, which include galactic-scale forces, gas
self-gravity, and supernova feedback. The statistical analysis suggests that,
even though purely gravitational effects are necessary to reproduce standard
observational laws, they are not sufficient in most cases. We show that the
extra injection of energy from supernova explosions plays a key role in
establishing the global turbulent field and the local dynamics and morphology
of molecular clouds. Additionally, we characterise structure function scaling
parameters as a result of cloud environmental conditions: some of the complexes
are immersed in diffuse (inter-arm) or dense (spiral-arm) environments, and
others are influenced by embedded or external supernovae. In quiescent regions,
we obtain time-evolving trajectories of scaling parameters driven by
gravitational collapse and supersonic turbulent flows. Our findings suggests
that a PCA-based statistical study is a robust method to diagnose the physical
mechanisms that drive the gravoturbulent properties of molecular clouds. Also,
we present a new open source module, the PCAFACTORY, which smartly performs PCA
to extract velocity structure functions from simulated or real data of the ISM
in a user-friendly way. Software DOI: 10.5281/zenodo.3822718
