Journal of Data Science

This paper discusses the coherent forecasting in two types of integervalued geometric autoregressive time series models of order one, viz., Geometric Integer-valued Autoregressive (GINAR(1)) model and New Geometric Integer-valued Autoregressive (NGINAR(1)) model. GINAR(1) model uses binomial thinning for the process generation, whereas, NGINAR(1) uses negative binomial thinning. The k-step ahead conditional probability mass function and the corresponding probability generating functions are derived. It is observed that for higher order lags, the conditional mean, variance and the probability generating functions of these two processes are close to each other, whereas, for lower order lags, they differ. The coherent forecasting performance of these models is studied with the help of simulated and real data sets.