Chapter 7 Exponential smoothing

Exponential smoothing was proposed in the late 1950s (Brown (1959), Holt (1957), and Winters (1960) are key pioneering works), and has motivated some of the most successful forecasting methods. Forecasts produced using exponential smoothing methods are weighted averages of past observations, with the weights decaying exponentially as the observations get older. In other words, the more recent the observation the higher the associated weight. This framework generates reliable forecasts quickly and for a wide range of time series, which is a great advantage and of major importance to applications in industry.

This chapter is divided into two parts. In the first part (Sections 7.17.4) we present the mechanics of the most important exponential smoothing methods, and their application in forecasting time series with various characteristics. This helps us develop an intuition to how these methods work. In this setting, selecting and using a forecasting method may appear to be somewhat ad hoc. The selection of the method is generally based on recognising key components of the time series (trend and seasonal) and the way in which these enter the smoothing method (e.g., in an additive, damped or multiplicative manner).

In the second part of the chapter (Section 7.5) we present the statistical models that underlie exponential smoothing methods. These models generate identical point forecasts to the methods discussed in the first part of the chapter, but also generate prediction intervals. Furthermore, this statistical framework allows for genuine model selection between competing models.

Bibliography

Brown, Robert Goodell. 1959. Statistical Forecasting for Inventory Control. McGraw/Hill.

Holt, Charles E. 1957. “Forecasting Seasonals and Trends by Exponentially Weighted Averages.” O.N.R. Memorandum 52. Carnegie Institute of Technology, Pittsburgh USA.

Winters, P R. 1960. “Forecasting Sales by Exponentially Weighted Moving Averages.” Management Science 6: 324–42.