Adaptive log-linear zero-inflated generalized poisson autoregressive model with applications to crime counts

Xiaofei Xu, Ying Chen, Cathy W.S. Chen*, Xiancheng Lin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


This research proposes a comprehensive ALG model (Adaptive Log-linear zero-inflated Generalized Poisson integer-valued GARCH) to describe the dynamics of integer-valued time series of crime incidents with the features of autocorrelation, heteroscedasticity, overdispersion and excessive number of zero observations. The proposed ALG model captures time-varying non-linear dependence and simultaneously incorporates the impact of multiple exogenous variables in a unified modeling framework. We use an adaptive approach to automatically detect subsamples of local homogeneity at each time point of interest and estimate the time-dependent parameters through an adaptive Bayesian Markov chain Monte Carlo (MCMC) sampling scheme. A simulation study shows stable and accurate finite sample performances of the ALG model under both homogeneous and heterogeneous scenarios. When implemented with data on crime incidents in Byron, Australia, the ALG model delivers a persuasive estimation of the stochastic intensity of criminal incidents and provides insightful interpretations on both the dynamics of intensity and the impacts of temperature and demographic factors for different crime categories.

Original languageEnglish
Pages (from-to)1493-1515
Number of pages23
JournalAnnals of Applied Statistics
Issue number3
Publication statusPublished - 2020
Externally publishedYes


  • Bayesian
  • Excess zeros
  • Integer-valued GARCH model
  • MCMC
  • Nonstationar-ity
  • Overdispersion

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Statistics, Probability and Uncertainty


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