Markov switching integer-valued generalized auto-regressive conditional heteroscedastic models for dengue counts

This study models weekly dengue case counts with two climatological variables: temperature and precipitation. Since conventional zero-inflated integer-valued generalized auto-regressive conditional heteroscedastic (GARCH) models and Poisson regression cannot properly illustrate consecutive 0s in time series of counts, the paper proposes a Markov switching Poisson integer-valued GARCH model wherein a first-order Markov process governs the switching mechanism. This newly designed model has some interesting statistical features: lagged dependence, overdispersion, consecutive 0s, non-linear dynamics and time varying coefficients for the meteorological variables governed by a two-state Markov chain structure. We perform parameter estimation and model selection within a Bayesian framework via a Markov chain Monte Carlo scheme. As an illustration, we conduct a simulation study to examine the effectiveness of the Bayesian method and analyse 12-year weekly dengue case counts from five provinces in north-eastern Thailand. The evidence strongly supports that the proposed Markov switching Poisson integer-valued GARCH model with two climatological covariates appropriately describes consecutive 0s, non-linear dynamics and seasonal patterns. The posterior probabilities deliver clear insight into the state changes that are captured in the data set modelled. We use predictive credible intervals for monitoring and for providing early warning signals of outbreaks.