Graphical Assistant Grouped Network Autoregression Model: A Bayesian Nonparametric Recourse

Abstract

Vector autoregression model is ubiquitous in classical time series data analysis. With the rapid advance of social network sites, time series data over latent graph is becoming increasingly popular. In this article, we develop a novel Bayesian grouped network autoregression model, which can simultaneously estimate group information (number of groups and group configurations) and group-wise parameters. Specifically, a graphically assisted Chinese restaurant process is incorporated under the framework of the network autoregression model to improve the statistical inference performance. An efficient Markov chain Monte Carlo sampling algorithm is used to sample from the posterior distribution. Extensive studies are conducted to evaluate the finite sample performance of our proposed methodology. Additionally, we analyze two real datasets as illustrations of the effectiveness of our approach.

Keywords:

• Graphical assistant Chinese restaurant process
• MCMC
• Mixture models
• Network data
• Vector autoregression

Supplementary Materials

All technique proofs, additional numerical results as well as another empirical application are given in the supplementary material.

Additional information

Funding

Yimeng Ren and Xuening Zhu are supported by the National Natural Science Foundation of China (nos. 71991472, 72222009, 11901105, U1811461). Xiaoling Lu is supported by the National Natural Science Foundation of China (nos. 72171229). Guanyu Hu is supported by the NSF Grant BCS-2152822 and DMS-2210371.