Adaptive Log-Linear Zero-Inflated Generalized Poisson Autoregressive Model with Applications to Crime Counts Data

• Activity Number: 83 - Applications in Surveys and Social Science
• Type: Contributed
• Date/Time: Sunday, July 28, 2019 : 4:00 PM to 5:50 PM
• Sponsor: Government Statistics Section
• Author(s): Xiaofei Xu* and Ying Chen and Xian-cheng Lin and Cathy W. S. Chen
• Companies: National University of Singapore-Faculity of Science and National University of Singapore and University of Science and Technology of China and Feng Chia University, Taichung, Taiwan
• Keywords: Time series of counts; Integer-valued GARCH model; Excess zeroes; Over-dispersion; Structural breaks; Markov chain Monte Carlo

Abstract

We propose a comprehensive ALG model (Adaptive Log-linear zero-inflated Generalised poisson integer-valued GARCH) to describe the dynamics of count series with features of autocorrelation, heteroscedasticity, over-dispersion and excessive number of zero observations. The proposed ALG model is of being able to flexibly capture the time-varying characteristics of the nonlinear responses and simultaneously incorporate the influence of exogenous variables in a unified modelling framework. The time-dependent parameters are automatically estimated under local subsamples identified through an adaptive MCMC procedure. Simulation study shows stable and accurate finite sample performance of the ALG model under both homogeneous and inhomogeneous situations. When being implemented to the crimes incidents data in Byron, Australia, the ALG model delivers insightful interpretations on the time evolution of the stochastic intensity and the impact of temperature on different criminal categories with various features. It shows that the temperature effect is not significant for ``malicious damage to property'' and ``arson'', yet relevant for ``liquor offences'' crimes with time-varying features.