High-order statistics have been proven useful in the framework of Convolutional Neural Networks (CNN) for a variety of computer vision tasks. In this paper, we propose to exploit high-order statistics in the framework of Recurrent Neural Networks (RNN) for skeleton-based hand gesture recognition. Our method is based on the Statistical Recurrent Units (SRU), an un-gated architecture that has been introduced as an alternative model for Long-Short Term Memory (LSTM) and Gate Recurrent Unit (GRU). The SRU captures sequential information by generating recurrent statistics that depend on a context of previously seen data and by computing moving averages at different scales. The integration of high-order statistics in the SRU significantly improves the performance of the original one, resulting in a model that is competitive to state-of-the-art methods on the Dynamic Hand Gesture (DHG) dataset, and outperforms them on the First-Person Hand Action (FPHA) dataset.