The paper develops a general flexible framework for Network Autoregressive Processes (NAR), wherein the response of each node 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, while the framework can accommodate heavier than Gaussian errors with both spatial-autorgressive and factor based 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 generalized least squares estimators for both a fixed, as well as a diverging number of network nodes, and also provide their ridge regularized counterparts that exhibit better performance in large network settings, together with their asymptotic distributions. 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.

翻译：文件为网络自动递减进程(NAR)制定了一个总体灵活框架,每个节点的响应线性取决于其过去的价值、相邻节点的事先指定的线性组合和一套节点特定的共变体。相应的系数是特定的节点,而框架则能够以空间-偏向性和因基共变结构来容纳比高斯错误更重的差错。我们提供了充分的条件,确保基本点点的稳定性(常态性),这种稳定性(常态性)大大低于文献中以往的对应方。此外,我们为固定的和不同数量的网络节点制定了普通和普遍的最低方位估计值,并提供在大型网络环境中表现较好的脊脊固定对应方,同时提供其无干扰分布。我们还解决了网络连接错误及其对上述各种NAR参数估计者无干扰分布的影响问题。框架在合成和真实空气污染数据上都作了说明。