A General Modeling Framework for Network Autoregressive Processes
A General Modeling Framework for Network Autoregressive Processes
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DOI：
10.1080/00401706.2023.2203184
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发表时间：
2021-10
期刊：
影响因子：
2.5
通讯作者：
Hang Yin;Abolfazl Safikhani;G. Michailidis
中科院分区：
文献类型：
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作者：
Hang Yin;Abolfazl Safikhani;G. Michailidis
摘要提出了一种网络自回归过程(NAR)的通用柔性框架，其中网络中每个节点的响应线性地依赖于它的过去值、相邻节点的预先指定的线性组合和一组特定于节点的协变量。相应的系数是特定于节点的，并且该框架可以利用空间自回归、基于因子或在某些设置下的一般协方差结构来适应比高斯更大的误差。我们提供了一个充分条件，以确保潜在的NAR的稳定性(平稳性)，它比文献中的同类工作弱得多。进一步，我们发展了固定数目和发散数目的网络节点的普通和(估计)广义最小二乘估计，并给出了它们在大型网络环境下表现出更好性能的岭正则估计及其渐近分布。我们得到了它们的渐近分布，可以用来检验从业者感兴趣的各种假设。我们还解决了错误指定网络连通性及其对各种NAR参数估计器的上述渐近分布的影响的问题。该框架以合成和真实的空气污染数据为例进行了说明。
ABSTRACT A general flexible framework for Network Autoregressive Processes (NAR) is developed, wherein the response of each node in the network linearly depends on its past values, a prespecified linear combination of neighboring nodes and a set of node-specific covariates. The corresponding coefficients are node-specific, and the framework can accommodate heavier than Gaussian errors with spatial-autoregressive, factor-based, or in certain settings general covariance structures. We provide a sufficient condition that ensures the stability (stationarity) of the underlying NAR that is significantly weaker than its counterparts in previous work in the literature. Further, we develop ordinary and (estimated) generalized least squares estimators for both fixed, as well as diverging numbers of network nodes, and also provide their ridge regularized counterparts that exhibit better performance in large network settings, together with their asymptotic distributions. We derive their asymptotic distributions that can be used for testing various hypotheses of interest to practitioners. We also address the issue of misspecifying the network connectivity and its impact on the aforementioned asymptotic distributions of the various NAR parameter estimators. The framework is illustrated on both synthetic and real air pollution data.