Title: Identifiability of VAR(1) model in a stationary setting Show Chinese title

Title: VAR(1)模型在平稳设定下的可识别性

Abstract: We consider a classical First-order Vector AutoRegressive (VAR(1)) model, where we interpret the autoregressive interaction matrix as influence relationships among the components of the VAR(1) process that can be encoded by a weighted directed graph. A majority of previous work studies the structural identifiability of the graph based on time series observations and therefore relies on dynamical information. In this work we assume that an equilibrium exists, and study instead the identifiability of the graph from the stationary distribution, meaning that we seek a way to reconstruct the influence graph underlying the dynamic network using only static information. We use an approach from algebraic statistics that characterizes models using the Jacobian matroids associated with the parametrization of the models, and we introduce sufficient graphical conditions under which different graphs yield distinct steady-state distributions. Additionally, we illustrate how our results could be applied to characterize networks inspired by ecological research. Show Chinese abstract

Abstract: 我们考虑一个经典的向量自回归（VAR(1））模型的一阶版本，在该模型中，我们将自回归交互矩阵解释为VAR(1)过程中各组成部分之间的影响力关系，并可以用加权有向图来编码。 大多数先前的工作基于时间序列观测研究了基于这些观测的图的结构可识别性，因此依赖于动态信息。 在这项工作中，我们假设存在平衡状态，转而研究从平稳分布识别图的可识别性，这意味着我们寻求一种方法，仅使用静态信息来重构动态网络背后的影响力图。 我们采用代数统计中的方法，利用与模型参数化相关的雅可比矩阵的拟阵来表征模型，并引入了足够的图形条件，使得不同的图产生不同的稳态分布。 此外，我们展示了我们的结果如何应用于表征受生态研究启发的网络。