High-order statistics have been proven useful inthe framework of Convolutional Neural Networks (CNN) fora variety of computer vision tasks. In this paper, we proposeto exploit high-order statistics in the framework of RecurrentNeural Networks (RNN) for skeleton-based hand gesture recog-nition. Our method is based on the Statistical Recurrent Units(SRU), an un-gated architecture that has been introduced as analternative model for Long-Short Term Memory (LSTM) andGate Recurrent Unit (GRU). The SRU captures sequential infor-mation by generating recurrent statistics that depend on a contextof previously seen data and by computing moving averages atdifferent scales. The integration of high-order statistics in theSRU significantly improves the performance of the original one,resulting in a model that is competitive to state-of-the-art methodson the Dynamic Hand Gesture (DHG) dataset, and outperformsthem on the First-Person Hand Action (FPHA) dataset.