Getting Started

Although exponential smoothing methods have been around since the 1950s, a modeling framework incorporating stochastic models, likelihood calculations, prediction intervals, and procedures for model selection was not developed until relatively recently, with the work of Ord et al. (1997) and Hyndman et al. (2002). In these (and other) papers, a class of state space models has been developed that underlies all of the exponential smoothing methods.

In this chapter, we provide an introduction to the ideas underlying exponential smoothing and the associated state space models.Many of the details will be skipped over in this chapter, but will be covered in later chapters.

Figure 2.1 shows the four time series from Fig. 1.1, along with point forecasts and 80% prediction intervals. These were all produced using exponential smoothing state space models. In each case, the particular models and all model parameters were chosen automatically with no intervention by the user. This demonstrates one very useful feature of state space models for exponential smoothing—they are easy to use in a completely automated way. In these cases, the models were able to handle data exhibiting a range of features, including very little trend, strong trend, no seasonality, a seasonal pattern that stays constant, and a seasonal pattern with increasing variation as the level of the series increases.