  Principal Component Analysis (PCA) is applied to a variety of blazars to
examine X-ray spectral variability. Data from nine different objects are
analysed in two ways: long-term, which examines variability trends across years
or decades, and short-term, which looks at variability within a single
observation. The results are then compared to simulated spectra in order to
identify the physical components that they correspond to. It is found that
long-term variability for all objects is dominated by changes in a single power
law component. The primary component is responsible for more than 84 per cent
of the variability in every object, while the second component is responsible
for at least 3 per cent. Small differences in the shapes of these components
can be used to predict qualities such as the degree to which spectral
parameters are varying relative to one another, and correlations between
spectral hardness and flux. Short-term variability is less clear-cut, with no
obvious physical analogue for some of the PCA results. We discuss the
simulation process, and specifically remark on the consequences of the
breakdown of the linearity assumption of PCA and how it manifests in the real
data. We conclude that PCA is a useful tool for analysing variability, but only
if its underlying assumptions and limitations are understood.
