Document Type : Original Scientific Paper
Department of Statistics, Yazd University, Yazd, Iran
In the real world, we may come across with zero-inflated or zero-deflated count data that have a very short-run autocorrelation. Integer-valued moving average processes are suitable for modeling these data. In this paper, a non-negative integer-valued moving average process of the first order with zero-modified geometric innovations is introduced. This model is called zero-modified geometric INMA(1) process which contains geometric INMA(1) process as a particular case. Some statistical properties of the process are obtained. The parameters of the model are estimated by the Yule-Walker method. Then, using the simulation study, we evaluate the performance of this estimators. Finally, the model is applied to two examples of real time series of the monthly number of rubella cases and the annually number of earthquakes magnitude 8.0 to 9.9. Then, we exhibit the ability of the model for fitting and predicting count data with excess and deficit of zeros.