Forecasting overdispersed INAR(1) count time series with negative binomial marginal

This paper addresses the coherent forecasting problem for overdispersed integer-valued autoregressive (INAR) model of order one having negative binomial marginal distribution. INAR models with Poisson or geometric marginal distribution have been used by several researchers to tackle the forecasting and related issues in low count time series. However, when the process results in relatively higher counts with overdispersion, these models do not provide satisfactory fit and good forecasts. We use negative binomial INAR(1) (NBINAR(1)) model for forecasting the count time series by deriving its exact forecast distribution. Extensive simulation study has been carried out to assess the performance of the forecasts obtained using NBINAR(1) with its INAR(1) counterparts. Two real data sets have been analyzed using the proposed methodology.