  We introduce a novel way to extract information from turbulent datasets by
applying an ARMA statistical analysis. Such analysis goes well beyond the
analysis of the mean flow and of the fluctuations and links the behavior of the
recorded time series to a discrete version of a stochastic differential
equation which is able to describe the correlation structure in the dataset. We
introduce a new intermittency parameter $\Upsilon$ that measures the difference
between the resulting analysis and the Obukhov model of turbulence, the
simplest stochastic model reproducing both Richardson law and the Kolmogorov
spectrum. We test the method on datasets measured in a von K\'arm\'an swirling
flow experiment. We found that the ARMA analysis is well correlated with
spatial structures of the flow, and can discriminate between two different
flows with comparable mean velocities, obtained by changing the forcing.
Moreover, we show that the intermittency parameter is highest in regions where
shear layer vortices are present, thereby establishing a link between
intermittency corrections and coherent structures. We show that some salient
features of the analysis are preserved when considering global instead of local
observables. Finally we analyze flow configurations with multistability
features where the ARMA technique is efficient in discriminating different
stability branches of the system.
