Learning of higher order temporal structures is central for times series analysis and sequential decision making.  It’s also relevant for the development of more efficient language models. In this contribution is introduced a mathematically rigorous model for the learning of temporal motifs of arbitrary large interaction order in binary sequential data. Conditions for the maximum likelihood and maximum entropy interactions parameters estimations are provided. It’s shown that if the resulting motifs parameters space is convex and with a closed affine boundary, then maximum likelihood and maximum entropy estimations are equivalent and can be calculated by exact algorithms. The implications of this result are explored in the context of sequential decision making applications.