Time series data involving counts are frequently encountered in many biomedical and public health applications. A problem occurs when count data have to be modeled. The number of counts in a certain period can only be an integer and that is why the commonly used ARMA model, which assumes stationarity, seems not very useful anymore, simply because there are some associated problems like outlier and over dispersion that can be encountered in the count data, which may actually lead to violation of stationarity assumption of the ARMA model. Thus, modeling this type of series requires one to choose the best model that can deal explicitly with the problem of the over-dispersion that can cause non-stationarity and/ or non-normality. The method of Integrated Autoregressive Moving Average (ARIMA) and Autoregressive Conditional Poisson (ACP) models were used to address the problem of the over-dispersion in the count data. The orders of the models were studied in respect to the level of over-dispersion and sample sizes through Monte Carlo simulation. The findings revealed that the ACP (2, 1) and ACP (1,2) are best at lower and higher sample sizes respectively when there is overdispersion. The forecast performance of ACP model increases as the steps ahead increases while that of ARIMA model declines.
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