Time series data often entail counts. Time series count data, which refer to the number of times an item or an event occurs within a fixed period of time, are essential in many fields most of the works on time series count data do not exhaustively consider the effect excess zeros in modeling. This study, therefore, seeks to examine the performance integer-valued autoregressive (INAR) and Poisson autoregressive models on count data under the influence of excess zeros. The effect of sample sizes, n =30, 60,…, 300, on the performance of the models were also studied. At every sample size, the best status of the orders p and q where p, q = 1, 2 are, respectively, determined for the levels of the excess zeros through simulations. The predictive ability of the models was observed at h-steps ahead, h = 5, 10, 15,…, 50 for the models with excess zeros data structures. It was concluded that the best model to fit and forecast data with excess zeros is INAR at different sample sizes. The predictive abilities of the four fitted models increased as sample size and number of steps ahead were increased