Context. The detection of exoplanets by direct imaging is an active research topic in astronomy. Even with the coupling of an extreme adaptive-optics system with a coronagraph, it remains challenging due to the very high contrast between the host star and the exoplanets.Aims. The purpose of this paper is to describe a method, named PACO, dedicated to source detection from angular differential imaging data. Given the complexity of the fluctuations of the background in the datasets, involving spatially variant correlations, we aim to show the potential of a processing method that learns the statistical model of the background from the data.Methods. In contrast to existing approaches, the proposed method accounts for spatial correlations in the data. Those correlations and the average stellar speckles are learned locally and jointly to estimate the flux of the (potential) exoplanets. By preventing from subtracting images including the stellar speckles residuals, the photometry is intrinsically preserved. A nonstationary multi-variate Gaussian model of the background is learned. The decision in favor of the presence or the absence of an exoplanet is performed by a binary hypothesis test.Results. The statistical accuracy of the model is assessed using VLT/SPHERE-IRDIS datasets. It is shown to capture the nonstationarity in the data so that a unique threshold can be applied to the detection maps to obtain consistent detection performance at all angular separations. This statistical model makes it possible to directly assess the false alarm rate, probability of detection, photometric and astrometric accuracies without resorting to Monte-Carlo methods.Conclusions. PACO offers appealing characteristics: it is parameter-free and photometrically unbiased. The statistical performance in terms of detection capability, photometric and astrometric accuracies can be straightforwardly assessed. A fast approximate version of the method is also described that can be used to process large amounts of data from exoplanets search surveys.