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The interaction of plasma gas with the surrounding atmosphere in plasma arc cutting (PAC) has been investigated using high-speed Schlieren imaging. The time series corresponding to the recorded intensity of each pixel have been postprocessed using statistical analysis. Two different methods that highlight the time variation of the amplitude of the fluctuations in the density field have been compared: the windowed standard deviation and the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) approach. Whereas a mean-variance analysis can provide at most time-averaged results, GARCH can model the instantaneous variation of the luminous signal, thus providing new insights on the time evolution of the turbulence around the arc.