Modeling zero-inflated and zero-deflated count data time series using the INMA(1) process

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.


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