A statistical-based approach for determining the intensity of unrest phases at Stromboli volcano (Southern Italy) using one-step-ahead forecasts of displacement time series

The evaluation of the intensity of unrest phases at active volcanoes is a crucial topic in volcano hazard studies. This is particularly troublesome in the case of persistently active volcanoes like Stromboli (Southern Italy), where intense eruptive summit activity (overflows, strong spattering, powerful explosions) has in some cases anticipated a flank eruption. In this context, a new approach for the analysis of displacement data is introduced. Daily displacements of the Stromboli crater terrace measured between January 1, 2010, and August 7, 2014, by a ground-based interferometric synthetic aperture radar system were compared, in retrospect, to displacement predictions provided by an autoregressive integrated moving average-based model. The methodology consisted in assessing when the actual displacements exceeded a fixed probability threshold for the forecasts (*95 %). Two sets of data were consequently produced: (1) series of residuals between actual displacements and model threshold (‘‘anomalies’’) and (2) series of normalized residuals between actual displacements and model threshold (‘‘normalized anomalies’’). This permitted to statistically identify and quantify the anomalous deformation at the crater terrace over the reference time interval of the analysis. Anomalies started to occur before each period of intense volcanic activity, highlighting the possibility to discern between background activity and unrest. Moreover, results indicated that the inflation of the crater terrace during the preparatory phase of the 2014 flank eruption was characterized by the greatest amount of anomalous deformation