Model Assisted Statistics and Applications 15 (2020) 1–17 1 DOI 10.3233/MAS-190475 IOS Press Modeling seasonal epidemic data using integer autoregressive model based on binomial thinning Manik Awale ∗ , A.S. Kashikar and T.V. Ramanathan Department of Statistics, Savitribai Phule Pune University, Pune, India Abstract. The epidemic surveillance data are always in the form of counts observed weekly, monthly or yearly. Integer Au- toregressive (INAR) models are the most suitable models for modeling such data. As most of the epidemic data has inherent seasonality in it, the INAR models need to be modified accordingly to take care of such seasonal behavior of the data. In this paper a seasonal geometric INAR(1) model based on binomial thinning is proposed with a seasonal period ‘s’ (GINAR(1)s). The thinning models based on binomial thinning are much easier to work with, than those based on negative binomial thinning, in terms of mathematical and computational complexity. Various inferential and probabilistic properties of the model are stud- ied. The forecasting ability of the GINAR(1)s model has been compared with that of the non seasonal counterparts. Extensive simulation study has been carried out to validate the coherent forecasting ability of the model. The model performs well for overdispersed low count time series data. The analysis of an epidemic data has been carried out to examine the performance of the proposed model. Keywords: Binomial thinning, coherent forecasting, geometric distribution, INAR models, seasonality 1. Introduction There are number of diseases which reoccur seasonally and affect the human life, which in turn brings burden to the economy of a country. Controlling epidemic outbreak and mass vaccination programs to counter these recurrence need lots of money and man power. Most of the epidemic surveillance data are count data and hence researchers use integer-valued autoregressive time series models for modeling such types of data. When there is an inherent seasonality in the series, the usual INtegar AutoRegressive (INAR) models will not give good forecasts. Hence, one has to take into consideration the seasonality in the data while proposing models. The literature on seasonality of epidemics dates back to Soper (1929), who studied the periodicity in disease prevalence in the case of local epidemics like Measles. He also claimed that infectivity changes seasonally. Season- ality in gastroenteritis and for influenza can be found in the work of Lossli et al. (1943). Even though the seasonal epidemic outbreaks were there since centuries, such types of data were recorded only from later part of 19 th century (see Serfling, 1963). A detailed discussion about the seasonal nature of emergence of various diseases can be found in Cook et al. (1990). The applicability of INAR models for modeling epidemic data has been discussed in Cardinal et al. (1999). Survival behavior of host, behavior of pathogen and host immune system are related to the seasonal variation (see Grassly & Fraser, 2006). Various contagious diseases exhibit seasonal patterns, a recent review on seasonality in Influenza and Respiratory Syncytial Virus (RSV) can be found in Bloom-Feshbach et al. (2013). * Corresponding author: Manik Awale, Department of Statistics, Savitribai Phule Pune University, Pune, India. E-mail: manik.stats@gmail. com. ISSN 1574-1699/20/$35.00 c  2020 – IOS Press and the authors. All rights reserved