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The analysis of JPEG compressed images is one of the most studied problems in image forensics, because of the extensive use and the characteristic traces left by such coding operation. In this paper, we propose a novel statistical framework for the identification of previous multiple aligned compressions in JPEG images and the estimation of the quality factors applied. The method has been tested on different datasets and forensic scenarios, where up to three JPEG compressions are considered. Moreover, both in the case of double and triple JPEG encoding with different quality factors, the compression history of each image is estimated. The experiments show good performance and, in most cases, higher accuracies with respect to state-of-the-art methods.