Modeling seasonal epidemic data using integer autoregressive model based on binomial thinning

Article type: Research Article

Authors: Awale, Manik^* | Kashikar, A.S. | Ramanathan, T.V.

Affiliations: Department of Statistics, Savitribai Phule Pune University, Pune, India

Correspondence: [*] Corresponding author: Manik Awale, Department of Statistics, Savitribai Phule Pune University, Pune, India. E-mail: [email protected].

Abstract: The epidemic surveillance data are always in the form of counts observed weekly, monthly or yearly. Integer Autoregressive (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 studied. 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

DOI: 10.3233/MAS-190475

Journal: Model Assisted Statistics and Applications, vol. 15, no. 1, pp. 1-17, 2020