modeling zero-inflated and zero-deflated count data time series using the inma(1) process

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.