  Binary random variables are the building blocks used to describe a large
variety of systems, from magnetic spins to financial time series and neuron
activity. In Statistical Physics the Kinetic Ising Model has been introduced to
describe the dynamics of the magnetic moments of a spin lattice, while in time
series analysis discrete autoregressive processes have been designed to capture
the multivariate dependence structure across binary time series. In this
article we provide a rigorous proof of the equivalence between the two models
in the range of a unique and invertible map unambiguously linking one model
parameters set to the other. Our result finds further justification
acknowledging that both models provide maximum entropy distributions of binary
time series with given means, auto-correlations, and lagged cross-correlations
of order one. We further show that the equivalence between the two models
permits to exploit the inference methods originally developed for one model in
the inference of the other.
