www.ajms.com 20 ISSN 2581-3463 RESEARCH ARTICLE On Performance of Integer-valued Autoregressive and Poisson Autoregressive Models in Fitting and Forecasting Time Series Count Data with Excess Zeros Saleh Ibrahim Musa 1 , N. O. Nwezeand 2 , M. O. Adenomon 2 1 Department of Statistics, Federal University of Lafia, PMB 146 Lafia, Nigeria, 2 Department of Statistics, Nasarawa State University Keffi, PMB 122 Keffi, Nigeria Received: 30-04-2021; Revised: 29-05-2021; Accepted: 26-06-2021 ABSTRACT 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 Key words: Count data, excess zeros, integer-valued autoregressive, Poisson autoregressive Address for correspondence: Saleh Ibrahim Musa E-mail: saleh.musa@science.fulafa.edu.ng INTRODUCTION Time series is the values of some statistical variables measured over a uniform set of time points. Examples of time series data are monthly sales in a store, monthly HIV/AIDS cases recorded in a hospital, yearly production by a company, daily number of eggs laid by fowls in a farm, consumption of electricity in kilowatts, and data on population motor registration per day. Time series data often entail counts, such as the number of road accidents, the number of patients in a certain hospital, and the number of customers waiting for service at a certain time. Count data can be found in many practical lifetime studies, such as the number of days before death in certain diseases or the number of cycles (runs) until a machine stops working and so on. Hence, a number of statistical distributions have been applied to model the case of a count random variable (RV) with a non-negative integer value. A good overview of these distributions can be found in Johnson et al. (2005). [9] Research in economics, ecology, environmental sciences, medical, and public health-related fields, it is often practical that the pattern of outcomes is relatively infrequent behaviors. Data of this type consist of excess zeros. It has been reported that the traditional Poisson model provided the popular frame work for fitting count data but not suitable for time series data with excess zeros and further considered using integer-valued autoregressive (INAR) (1) model with restricted application to zeros and ones data (Qi et al., 2019). [21] Data with many zeros are usually frequent in research studies when counting the occurrence of certain behavioral events, such as number of purchases made, number of school absences, number of cigarettes smoked, or number of hospitalizations. These types of data are called count data and their values are usually non-negative with a lower bound of zero. Common issues when dealing with count data are typically zero inflation or excessive zeros (Akeyede et al., 2021). [1]