We propose an autoregressive framework for modelling dynamic networks with dependent edges. It encompasses the models which accommodate, for example, transitivity, density-dependent and other stylized features often observed in real network data. By assuming the edges of network 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 the straightforward manner. Due to the possible large number of parameters in the models, the initial MLEs may suffer from slow convergence rates. An improved estimator for each component parameter is proposed based on an iteration based on the projection which mitigates the impact of the other parameters (Chang et al., 2021, 2023). Based on a martingale difference structure, the asymptotic distribution of the improved estimator is derived without the stationarity assumption. The limiting distribution is not normal in general, and 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：我们提出一种用于建模边依赖动态网络的自回归框架。该框架涵盖了能够容纳真实网络数据中常见特征（如传递性、密度依赖性及其他典型特征）的模型。通过假设每个时刻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（TERGMs）具有紧密联系，并可直接支持模拟与极大似然估计。由于模型中可能存在大量参数，初始极大似然估计量（MLEs）可能收敛速度较慢。基于投影迭代方法（Chang et al., 2021, 2023），我们提出针对各分量参数的改进估计量，以降低其他参数的影响。借助鞅差结构，我们在无需平稳性假设的条件下推导出改进估计量的渐近分布。该极限分布通常非正态，而当基础过程满足某些混合条件时，极限分布退化为正态分布。通过传递性模型，我们分别在模拟实验和真实网络数据集上进行了验证。