Exponential Smoothing

Exponential smoothing methods generate forecasts using the more recent information from a time series, similar to a moving average smoother, except that the weights are not equal; the more recent observations are weighted more heavily than other observations.

References

• Forecasting and Time Series - An Applied Approach (Bowerman) chapter 8 (Third Edition)

• Introduction to Time Series Analysis and Forecasting (Montgomery) chapter 4

• Use R Introductory Time Series with R (Cowpertwait) section 3.4

Resources

• Forecasting: principles and practice (Hyndman)

• NIST - Exponential Smoothing

Considerations when fitting an exponential smoothing model.

• Selection of initial conditions (y0).

• Selection of smoothing constants.

• Optimization of some model fitting criteria.

Smoothing constants are sometimes selected by choosing the value of the constant that minimizes the one-step-ahead forecast error terms, squared forecast error, or similar criteria.

• (NOTE: This is different than minimizing within-sample error.)

For simple exponential smoothing, the value of the smoothing constant is often between 0.01 and 0.30.

• Bowerman recommends (p. 386) that if the chosen value of the smoothing constant is greater than 0.3, some other method should be considered.

Caution regarding exponential smoothing models:

From Chapter 8 of Forecasting and Time Series - An Applied Approach (Bowerman) p. 379 (Third Edition)

"It is important to note that exponential smoothing methods are not based on any formal statistical model or statistical theory. Rather, these techniques are intuitive methods that produce adequate forecasts in some applications. Since these methods have been developed in a piecemeal fashion, no formal statistical methodology exists for building an exponential smoothing model. In fact, some practitioners strongly object to using the term 'model' in the context of exponential smoothing."

Which type of exponential smoothing to use?

• For time series with a constant level over time (no increasing or decreasing trend or seasonality), then simple (single) exponential smoothing may suffice.

• For time series with a trend, second-order (double) exponential smoothing may be considered.

• For time series with a trend and/or some type of seasonal or cyclic behavior, then the Holt-Winters' (aka Winters') method may be used.

• There are additive and multiplicative methods.

Hyndman provides a table (Table 7.8) showing 15 different varieties of exponential smoothing

Types of exponential smoothing models include:

EWMA