Contemporary time series data often feature objects connected by a social network that naturally induces temporal dependence involving connected neighbours. The network vector autoregressive model is useful for describing the influence of linked neighbours, while recent generalizations aim to separate influence and homophily. Existing approaches, however, require either correct specification of a time series model or accurate estimation of a network model or both, and rely exclusively on least-squares for parameter estimation. This paper proposes a new autoregressive model incorporating a flexible form for latent variables used to depict homophily. We develop a first-order differencing method for the estimation of influence requiring only the influence part of the model to be correctly specified. When the part including homophily is correctly specified admitting a semiparametric form, we leverage and generalize the recent notion of neighbour smoothing for parameter estimation, bypassing the need to specify the generative mechanism of the network. We develop new theory to show that all the estimated parameters are consistent and asymptotically normal. The efficacy of our approach is confirmed via extensive simulations and an analysis of a social media dataset.

翻译：当代时间序列数据通常具有由社交网络连接的实体特征，这种网络结构自然会导致相邻节点间产生时序依赖关系。网络向量自回归模型能有效描述关联邻居的影响，而近年来的推广研究旨在区分影响力效应与同质性效应。然而现有方法要么需要正确设定时间序列模型，要么需要准确估计网络模型，甚至两者兼需，且参数估计完全依赖最小二乘法。本文提出一种新型自回归模型，通过引入灵活形式的潜变量来刻画同质性效应。我们开发了一阶差分方法用于估计影响力效应，该方法仅需模型中的影响力部分被正确设定。当包含同质性的模型部分正确设定为半参数形式时，我们借鉴并推广了近期提出的邻居平滑概念进行参数估计，无需指定网络的生成机制。我们建立了新的理论框架，证明所有估计参数均具有一致性和渐近正态性。通过大规模仿真实验和社交媒体数据集分析，我们验证了该方法的有效性。