The paper introduces a flexible model for the analysis of multivariate nonlinear time series data. The proposed Functional Coefficients Network Autoregressive (FCNAR) model considers the response of each node in the network to depend in a nonlinear fashion to each own past values (autoregressive component), as well as past values of each neighbor (network component). Key issues of model stability/stationarity, together with model parameter identifiability, estimation and inference are addressed for error processes that can be heavier than Gaussian for both fixed and growing number of network nodes. The performance of the estimators for the FCNAR model is assessed on synthetic data and the applicability of the model is illustrated on multiple indicators of air pollution data.

翻译：本文提出了一种用于分析多元非线性时间序列数据的灵活模型。所提出的函数系数网络自回归（FCNAR）模型考虑网络中每个节点的响应以非线性方式依赖于自身历史值（自回归分量）以及每个邻居的历史值（网络分量）。针对误差过程可能比高斯分布更重尾的情形，本文在固定及递增网络节点数下探讨了模型稳定性/平稳性、模型参数可识别性、估计与推断等关键问题。通过合成数据评估了FCNAR模型估计量的性能，并利用空气污染数据的多个指标展示了该模型的适用性。