We propose an autoregressive framework for modelling dynamic networks with dependent edges. It encompasses models that accommodate, for example, transitivity, degree heterogenenity, and other stylized features often observed in real network data. By assuming the edges of networks at each time are independent conditionally on their lagged values, the models, which exhibit a close connection with temporal ERGMs, facilitate both simulation and the maximum likelihood estimation in a straightforward manner. Due to the possibly large number of parameters in the models, the natural MLEs may suffer from slow convergence rates. An improved estimator for each component parameter is proposed based on an iteration employing projection, which mitigates the impact of the other parameters (Chang et al., 2021; Chang et al., 2023). Leveraging a martingale difference structure, the asymptotic distribution of the improved estimator is derived without the assumption of stationarity. The limiting distribution is not normal in general, although it reduces to normal when the underlying process satisfies some mixing conditions. Illustration with a transitivity model was carried out in both simulation and a real network data set.

翻译：我们提出一个用于建模动态网络中相依边的自回归框架。该框架包含能容纳传递性、度异质性及其他真实网络数据中常见典型特征的模型。通过假定每个时间点上的网络边在给定其滞后值条件下独立，这些模型与时间指数随机图模型存在紧密联系，并能够以直接的方式同时进行模拟和极大似然估计。由于模型中可能包含大量参数，自然的最大似然估计量可能收敛速度较慢。我们基于投影迭代方法（Chang et al., 2021; Chang et al., 2023）提出改进的分量参数估计量，以减轻其他参数的影响。利用鞅差结构，我们在无需平稳性假设的条件下推导了改进估计量的渐近分布。该极限分布通常非正态，但当底层过程满足某些混合条件时退化为正态分布。我们通过传递性模型的模拟实验和真实网络数据集进行了验证。