Negative Binomial tv-DINGARCH Models for Monthly DHF Cases in Surabaya, Indonesia (2015-2025) - Aminatuz Zahro; A'yunin Sofro (CAUCHY: Jurnal Matematika Murni dan Aplikasi, 2026)
Count time series data are commonly encountered in epidemiological studies, such as monthly reports of Dengue Hemorrhagic Fever (DHF) cases. The INGARCH model has been widely used to handle temporal dependence and overdispersion in such data. However, the standard INGARCH model assumes constant dispersion, whereas in practice the dispersion level may vary over time due to epidemiological factors like seasonality or vector control policies. Accurately capturing this time-varying variability is essential for reliable disease surveillance. This study applies the tv-DINGARCH model to DHF cases in Surabaya from January 2015 to December 2025. The tv-DINGARCH(1,1,1,1) model with Negative Binomial distribution is used because it allows the dispersion parameter \(φ_t\) to evolve dynamically. Parameter estimation is conducted using the Conditional Maximum Likelihood Estimation method implemented in RStudio. The results show that the tv-DINGARCH model yields AIC = 968.43 and BIC = 985.68, both smaller than those of the standard INGARCH model (AIC = 1012.18, BIC = 1023.68). The likelihood ratio test produces an LR statistic of 47.7560 with a p-value less than 0.000001, strongly rejecting constant dispersion. The stationarity condition is satisfied with \(β_2 + α_2 + β_1 + α_1 = 0.9990 1\). From a public health perspective, these findings indicate that the tv-DINGARCH model better captures the fluctuating dynamics of DHF transmission, supporting more effective surveillance and early warning systems.