ARIMA models and exponential smoothing

Exponential smoothing is one of many approaches to analyzing time series data. It is usually applied to modeling the trend component of time series (it can, however, be used for other components of time series as well) which are not stable over time and change rapidly. If this is the case, the usual decomposition cannot be used and other ways of modeling are sought, such as ARIMA or other stochastic models. There is, however, a connection between the two. In this paper we show that for most of the exponential smoothing models an ARIMA counterpart exists (and vice versa). The theoretical duality of these models is shown, including some inference. Both models are applied to simulated data in several software packages (SAS, eViews, and Statgraphics) and the results are compared. This way the issue is illuminated to the readers, who are then able to compare the considered software packages when working with similar models.