Autoregressive networks

Binyan Jiang, Jialiang Li and Qiwei Yao

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

Abstract: We propose a rst-order autoregressive (i.e. AR(1)) model for dynamic network processes in which edges change over time while nodes remain unchanged. The model depicts the dynamic changes explicitly. It also facilitates simple and ecient statistical inference methods including a permutation test for diagnostic checking for the tted network models. The proposed model can be applied to the network processes with various underlying structures but with independent edges. As an illustration, an AR(1) stochastic block model has been investigated in depth, which characterizes the latent communities by the transition probabilities over time. This leads to a new and more eective spectral clustering algorithm for identifying the latent communities. We have derived a nite sample condition under which the perfect recovery of the community structure can be achieved by the newly dened spectral clustering algorithm. Furthermore the inference for a change point is incorporated into the AR(1) stochastic block model to cater for possible structure changes. We have derived the explicit error rates for the maximum likelihood estimator of the change-point. Application with three real data sets illustrates both relevance and usefulness of the proposed AR(1) models and the associate inference methods.

Keywords: AR(1) networks; change point; dynamic stochastic block model; Hamming distance; maximum likelihood estimation; spectral clustering algorithm; Yule-Walker equation (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Date: 2023-08-15
New Economics Papers: this item is included in nep-ecm and nep-net
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Published in Journal of Machine Learning Research, 15, August, 2023. ISSN: 1532-4435

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