Selecting Best Arima Model for Poison Data at Different Parameter Values

A problem occurs when poison data have to be modeled. The number of counts in a certain period can only be an integer that is why the commonly used Autoregressive Moving Average (ARMA) model in time series, 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 poison data. For this problem, Integrated Autoregressive Moving Average (ARIMA) models were studied. These models were used to capture poison data with different phenomena. Data set were simulated from poison process with λ = 5, 10 and 20. ARIMA (p, q) were then fitted to the simulated data so as to examine the effect of the changes in parameter value of the poison on the models0 performance across the sample size. It was concluded that ARIMA (2,1,2) and ARIMA (1,1,2) are obviously the best at lower and higher sample sizes respectively.