Grouped Network Poisson Autoregressive Model

Abstract

Multivariate Poisson autoregressive models are common ways to fit count time series data, while the statistical inference is quite challenging. The network Poisson autoregressive model (NPAR) reduces the inference complexity by incorporating network information into the dependence structure, where the response of each individual can be explained by its lagged values and the average effect of its neighbors. However, NPAR makes one strong assumption that all individuals are homogeneous and they share a common autoregressive coefficient. Here we propose a grouped network Poisson autoregressive model (GNPAR), where the individuals are classified into different groups with group-specific parameters to describe heterogeneous nodal behaviors. We present the stationarity and ergodicity of the GNPAR model and study the asymptotic properties of the maximum likelihood estimation.We develop an EM algorithm to estimate the unknown group labels and investigate the finitesample performance of our estimation procedure using simulations. We analyze the Chicago Police Investigatory Stop Report data and find distinct dependence patterns in different neighborhoods of Chicago that could be potentially helpful for future crime prevention.

A Systematic Review of INGARCH Models for Integer-Valued Time Series

“…This is a somewhat detached assumption from reality. Therefore, Tao et al [ 31 ] proposed the grouped PNAR, which divides individuals into different groups and describes heterogeneous node behavior with group-specific parameters. Compared to the original PNAR model, the constraints are relaxed while competently portraying the heterogeneity.…”

“…Compared to the original PNAR model, the constraints are relaxed while competently portraying the heterogeneity. Specially, all individuals could be classified into K groups in the setting of Tao et al [ 31 ], and each group was characterized by a specific set of positive parameters , for .…”

“…Lee et al [ 25 ], Kim et al [ 26 ] and Cui and Zhu [ 27 ] focus on the INGARCH-type models for bivariate count times series, but, subject to the development of multivariate Poisson distribution, more multivariate models related to these studies have not been extended. Another emerging area is the INGARCH-type models for time-varying network data (Armillotta and Fokianos [ 28 ], Armillotta et al [ 29 ], Armillotta and Fokianos [ 30 ] and Tao et al [ 31 ]), and many of the attempts that come with the challenge are worthwhile, such as optimization of conditional distributions, nonlinear dynamic structures and time-varying network data with upper bounds on the number of edges.…”

Softplus negative binomial network autoregression

“…The Poisson NAR (PNAR) model proposed by Armillotta and Fokianos (2024) is an extension of the continuous‐valued NAR model, and they gave the parameter estimates of the model using maximizing the quasi‐likelihood function and discussed the asymptotic property of the parameter estimates as . Based on Zhu and Pan (2020) and Armillotta and Fokianos (2024), Tao et al (2024) proposed a grouped PNAR model and studied its stationarity and ergodicity and the asymptotic properties of the maximum likelihood estimator (MLE).…”

“…∞. Based on Zhu and Pan (2020) and Armillotta and Fokianos (2024), Tao et al (2024) proposed a grouped PNAR model and studied its stationarity and ergodicity and the asymptotic properties of the maximum likelihood estimator (MLE).…”