Forecast horizon aggregation in integer autoregressive moving average (INARMA) models

This paper addresses aggregation in integer autoregressive moving average (INARMA) models. Although aggregation in continuous-valued time series has been widely discussed, the same is not true for integer-valued time series. Forecast horizon aggregation is addressed in this paper. It is shown that the overlapping forecast horizon aggregation of an INARMA process results in an INARMA process. The conditional expected value of the aggregated process is also derived for use in forecasting. A simulation experiment is conducted to assess the accuracy of the forecasts produced by the aggregation method and to compare it to the accuracy of cumulative h-step ahead forecasts over the forecasting horizon. The results of an empirical analysis are also provided.

► We address the forecast horizon aggregation in INARMA processes.
► The conditional mean of the aggregated process for the general INARMA(p,q) process is obtained.
► We show that the aggregation of an INARMA process over a horizon results in an INARMA process.
► Accuracy of the aggregated forecasts based on two approaches is compared for INAR(1), INMA(1) and INARMA(1,1) processes.
► Performance of these forecasts is also tested on empirical data.