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

Aishwarya Ghodake (), Manik Awale, Hassan S. Bakouch, Gadir Alomair () and Amira F. Daghestani
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Aishwarya Ghodake: Department of Statistics, Savitribai Phule Pune University, Pune 411007, India
Manik Awale: Department of Statistics, Savitribai Phule Pune University, Pune 411007, India
Hassan S. Bakouch: Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
Gadir Alomair: Department of Quantitative Methods, School Business, King Faisal University, Al-Ahsa 31982, Saudi Arabia
Amira F. Daghestani: Department of Mathematics, College of Science and Humanities, Imam Abdulrahman Bin Faisal University, Jubail 35811, Saudi Arabia

Mathematics, 2025, vol. 13, issue 15, 1-31

Abstract: 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.

Keywords: autoregression; binomial thinning; coherent forecasting; count time series; seasonality; simulation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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