Autoregressive networks with dependent edges

Jinyuan Chang, Qin Fang, Eric D. Kolaczyk, Peter W. MacDonald and Qiwei Yao

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

Abstract: 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 exponential random graph models, facilitate both simulation and the maximum likelihood estimation (MLE) 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. 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.

Keywords: conditional independence; dynamic networks; maximum likelihood estimation; stylized features of network data; transitivity (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Pages: 20 pages
Date: 2026-04-16
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Published in Journal of the Royal Statistical Society. Series B: Statistical Methodology, 16, April, 2026. ISSN: 1369-7412

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