Count Data in Time Series

This research paper is about time series of count data. The common methods, like the Autoregressive Moving Average model, are not profitable to use, because they do not account for integer-valued positive numbers. That is why other methods will be proposed. The Integervalued Autoregressive model and the newly suggested Autoregressive Conditional Integer-valued model will be explained and compared. This article concludes three things: the theoretically best method to use with count data is the ACI-model, because of few violated assumptions, such as possibly negative correlations and the assumption of the presence of a Poisson distribution; the best method on the basis of a simulation study is the INAR-model, shown by the fact that this model is even doing good when data is simulated by another method; the best method for particular purchase data is the Poisson-model, but that is mostly due to the low existence of autocorrelation. All in all, the INAR-model seems most useful for time series of count data.