A Seasonal Transmuted Geometric INAR Process: Modeling and Applications in Count Time Series

In this paper, the authors introduce the transmuted geometric integer-valued autoregressive model with periodicity, designed specifically to analyze epidemiological and public health time series data. The model uses a transmuted geometric distribution as a marginal distribution of the process. It also captures varying tail behaviors seen in disease case counts and health data. Key statistical properties of the process, such as conditional mean, conditional variance, etc., are derived, along with estimation techniques like conditional least squares and conditional maximum likelihood. The ability to provide k-step-ahead forecasts makes this approach valuable for identifying disease trends and planning interventions. Monte Carlo simulation studies confirm the accuracy and reliability of the estimation methods. The effectiveness of the proposed model is analyzed using three real-world public health datasets: weekly reported cases of Legionnaires’ disease, syphilis, and dengue fever.