论文标题
关于动力学模型与离散自回归过程之间的等效性
On the equivalence between the Kinetic Ising Model and discrete autoregressive processes
论文作者
论文摘要
二进制随机变量是用于描述从磁性旋转到财务时间序列和神经元活动的各种系统的构建块。在统计物理学中，已经引入了动力学模型来描述旋转晶格的磁矩的动力学，而在时间序列分析中，已设计了离散自回归过程，以捕获跨二进制时间序列的多元依赖性结构。在本文中，我们提供了一个严格的证明，证明了两个模型之间在独特且可逆的地图范围内明确链接一个模型参数的范围。我们的结果发现进一步的理由确认，这两种模型都提供了给定的均值，自动相关和滞后订单的滞后二进制时间序列的最大熵分布。我们进一步表明，这两个模型之间的等效性允许利用最初针对另一个模型开发的推理方法。
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.
