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.