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.

二元随机变量是用于描述各种系统的构建块，从磁自旋到金融时间序列和神经元活动。在统计物理学中，引入了动力学 Ising 模型来描述自旋晶格的磁矩动力学，而在时间序列分析中，离散自回归过程被设计为捕获跨二进制时间序列的多元相关结构。在本文中，我们在唯一且可逆的映射范围内提供了两个模型之间的等价性的严格证明，该映射明确地将一个模型参数集链接到另一个模型参数集。我们的结果找到了进一步的理由，承认两个模型都提供了具有给定均值、自相关和一阶滞后互相关的二进制时间序列的最大熵分布。