Autoregressive Networks with Dependent Edges

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.