Bayesian inference for integer-valued time series models with applications

Abstract

?Modelling integer-valued time series and its applications has become increasingly important for research in epidemiology, environmental science, public health, etc. The goal of this talk is to give a brief review on the recent developments of modelling time series of counts and to provide Bayesian inferences, diagnostics, model comparisons, and forecasting. I shall cover two major topics. 1)???? The causal relationship between climate and criminal behavior (Chen and Lee 2017): Reflecting the characteristic of an integer-valued chronological sequence of crime counts, we propose a modified Granger causality test based on the GARCH type of integer-valued time series models to analyze the relationship between the number of crimes and the temperature as an environmental factor. The posterior probability helps to determine the causality between the variables considered. Our findings show that hot months give rise to more sexual offenses, drug offenses and domestic-violence-related assaults than do the other seasons of the year in Ballina, Australia. This information can greatly help the authorities to take proper action for crime prevention and reduction. 2)???? Modelling weekly dengue case counts with climatological variables (Chen et al. 2019): We propose a Markov switching Poisson integer-valued GARCH model and investigate statistical properties of this new model. This newly designed model has some interesting features, including lagged dependence, overdispersion, consecutive 0’s, non-linear dynamics, and time varying coefficients for meteorological variables governed by a two-state Markov chain structure. We perform parameter estimation and model selection via adaptive Markov chain Monte Carlo sampling schemes, conduct a simulation study to examine the effectiveness of the Bayesian method, and analyze 12-year weekly dengue case counts from five provinces in northeastern Thailand. The posterior probabilities deliver clear insight into the state changes that are captured in the dataset modelled. The impact of this development is to offer practitioners an approach to use predictive credible intervals for monitoring and for providing early warning signals of dengue outbreaks. ? References Chen*, C.W.S., Khamthong, K. (Ph.D. st), and Lee, S. (2019) Markov switching integer-valued generalized auto-regressive conditional heteroscedastic models for dengue counts, Journal of the Royal of Statistical Society Series C – Applied Statistics, 68, 963–983. Chen*, C.W.S. and Lee, S. (2017) Bayesian causality test for integer-valued time series models with applications to climate and crime data, Journal of the Royal of Statistical Society Series C – Applied Statistics, 66, 797-814.