Fitting multivariate autoregressive (AR) models is fundamental for time-series data analysis in a wide range of applications. This article considers the problem of learning a $p$ -lag multivariate AR model where each time step involves a linear combination of the past $p$ states followed by a probabilistic, possibly nonlinear, mapping to the next state. The problem is to learn the linear connectivity tensor from observations of the states. We focus on the sparse setting, which arises in applications with a limited number of direct connections between variables.