@article{a5a994480bf74ff6b1aee3f869a6768b,
title = "Adaptive log-linear zero-inflated generalized poisson autoregressive model with applications to crime counts",
abstract = "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.",
keywords = "Bayesian, Excess zeros, Integer-valued GARCH model, MCMC, Nonstationar-ity, Overdispersion",
author = "Xiaofei Xu and Ying Chen and Chen, {Cathy W.S.} and Xiancheng Lin",
note = "Funding Information: We thank the Editor, the Associate Editor and anonymous referees for their valuable time and careful comments, which have helped improve this paper. The authors gratefully acknowledge the financial support of Singapore{\textquoteright}s Ministry of Education Academic Research Fund Tier 1 and Institute of Data Science at National University of Sin-gapore. Cathy W. S. Chen{\textquoteright}s research is funded by the Ministry of Science and Technology, Taiwan (grant MOST 107-2118-M-035-005-MY2). Funding Information: Acknowledgments. We thank the Editor, the Associate Editor and anonymous referees for their valuable time and careful comments, which have helped improve this paper. The authors gratefully acknowledge the financial support of Singapore{\textquoteright}s Ministry of Education Academic Research Fund Tier 1 and Institute of Data Science at National University of Singapore. Cathy W. S. Chen{\textquoteright}s research is funded by the Ministry of Science and Technology, Taiwan (grant MOST 107-2118-M-035-005-MY2). Publisher Copyright: {\textcopyright} Institute of Mathematical Statistics, 2020.",
year = "2020",
doi = "10.1214/20-AOAS1360",
language = "English",
volume = "14",
pages = "1493--1515",
journal = "Annals of Applied Statistics",
issn = "1932-6157",
publisher = "Institute of Mathematical Statistics",
number = "3",
}