Chapter 17. Smoothing Methods
In this chapter we describe popular, flexible methods for forecasting time series that rely on smoothing. Smoothing is based on averaging over multiple observations in order to reduce the noise. We start with two simple smoothers, the moving average and simple exponential smoother, which are suitable for forecasting series that contain no trend or seasonality. In both cases forecasts are averages of previous values of the series (the length of the series history that is considered and the weights that are used in the averaging differ between the methods). We also show how a moving average can be used, with a slight adaptation, for data visualization. We then proceed to describe smoothing methods that are suitable for forecasting series with a trend and/or seasonality. Smoothing methods are data driven and are able to adapt to changes in the series over time. Although highly automated, the user must specify smoothing constants, which determine how fast the method adapts to new data. We discuss the choice of such constants and their meaning. The different methods are illustrated using the Amtrak ridership series.
A second class of methods for time series forecasting are smoothing methods. Unlike regression models, which rely on an underlying theoretical model for the components of a time series (e.g., linear model or multiplicative seasonality), smoothing methods are data driven in the sense that they estimate time series components directly ...