Endowing visual agents with predictive capability is a key step towards video intelligence at scale. The predominant modeling paradigm for this is sequence learning, mostly implemented through LSTMs. Feed-forward Transformer architectures have replaced recurrent model designs in ML applications of language processing and also partly in computer vision. In this paper we investigate on the competitiveness of Transformer-style architectures for video predictive tasks. To do so we propose HORST, a novel higher order recurrent layer design whose core element is a spatial-temporal decomposition of self-attention for video. HORST achieves state of the art competitive performance on Something-Something early action recognition and EPIC-Kitchens action anticipation, showing evidence of predictive capability that we attribute to our recurrent higher order design of self-attention.