Hand gestures are the most natural and intuitive non-verbal communication medium while interacting with a computer, and related research efforts have recently boosted interest. Additionally, the identifiable features of the hand pose provided by current commercial inexpensive depth cameras can be exploited in various gesture recognition based systems, especially for Human-Computer Interaction. In this paper, we focus our attention on 3D dynamic gesture recognition systems using the hand pose information. Specifically, we use the natural structure of the hand topology-called later hand skeletal data-to extract effective hand kinematic descriptors from the gesture sequence. Descriptors are then encoded in a statistical and temporal representation using respectively a Fisher kernel and a multi-level temporal pyramid. A linear SVM classifier can be applied directly on the feature vector computed over the whole presegmented gesture to perform the recognition. Furthermore, for early recognition from continuous stream, we introduced a prior gesture detection phase achieved using a binary classifier before the final gesture recognition. The proposed approach is evaluated on three hand gesture datasets containing respectively 10, 14 and 25 gestures with specific challenging tasks. Also, we conduct an experiment to assess the influence of depth-based hand pose estimation on our approach. Experimental results demonstrate the potential of the proposed solution in terms of hand gesture recognition and also for a low-latency gesture recognition. Comparative results with state-of-the-art methods are reported.