A model for integer-valued time series with conditional overdispersion

In this paper, a new model, motivated by the weekly dengue cases in Singapore from year 2001 to 2010, is proposed to handle the conditional equidispersion, overdispersion and underdispersion in integer-valued pure time series. It is shown that the INARCH model studied by earlier researchers is a special case. Conditions for weak and strict stationarity of this model are also given in our paper. Some basic properties of this model are shown to be parallel to those of the classical autoregressive model. Three distribution based methods and two non-distribution based methods are presented for parameter estimation. These methods are compared in a simulation study for the conditional overdispersed situation with an integer-valued pure time series of order one. Finally, this model is applied to the motivating example.