Bayesian Vector Zero-Inflated Count Model; A Time Series Model for Covid-19 Variables

This study addresses the challenges of modeling multivariate time series data arising from the COVID-19 pandemic, characterized by overdispersion, zero inflation, and dynamic interdependencies among key indicators such as new cases, death cases, and recoveries. The aim is to develop and evaluate advanced statistical models that can accurately capture these complexities for improved surveillance and forecasting. The methodology adopts a Bayesian framework to estimate both Vector Linear and Log-Linear Zero-Inflated Negative Binomial INGARCH (ZINB-INGARCH) models. The data consist of daily reported COVID-19 cases, deaths, and recoveries from 2020 to 2023. Bayesian Markov Chain Monte Carlo (MCMC) methods were employed to estimate model parameters, using prior distributions tailored for overdispersed and zero-inflated count data. Results showed that the Log-Linear ZINB-INGARCH model performed better than the linear variant in terms of parameter significance, stationarity, and dynamic stability. Particularly, stationarity parameters in the log-linear model (e.g., d3=−0.507, 95% HDI: [-0.990, -0.020]) demonstrated clear evidence of mean reversion, while autoregressive coefficients such as A[3,3]=0.150, (HDI: [0.074, 0.200]) confirmed strong self-excitation. The dispersion parameters ϕ1=2.793, ϕ2=2.903, and ϕ3=2.116 further confirmed the presence of significant overdispersion. In contrast to the linear model’s higher zero-inflation rates ( ), the log-linear model revealed minimal zero-inflation probabilities around πi ​≈0.019, indicating better fit to structural zeros in the data. Residual diagnostics supported these results, with Ljung-Box p-values of 1.000 indicating successful modeling of temporal dependencies. The study provides robust empirical evidence that log-linear ZINB-INGARCH models are more effective in capturing the statistical properties of COVID-19 data, offering improved tools for policymakers and epidemiologists in managing future public health crises.