Chapter 6 Exponential smoothing method and ETS

We start our discussion of exponential smoothing with the original Simple Exponential Smoothing (SES) forecasting method, which was formulated by (Brown 1956): \[\begin{equation} \hat{y}_{t+1} = \alpha {y}_{t} + (1 - \alpha) \hat{y}_{t}, \tag{6.1} \end{equation}\]

where \(\alpha\) is the smoothing parameter, defined by analyst and which is typically restricted with (0, 1) region (this region is actually arbitrary and we will see later what is the correct one). This is one of the simplest forecasting method, and the smoothing parameter in it is typically interpretted as a weight between the actual value and the one-step-ahead predicted one. It is a recursive method, meaning that there needs to be some starting point \(\hat{y}_1\) in order to apply (6.1) to the existing data.

If you are interested in more details about the exponential smoothing and its history, the reviews (Gardner 1985) and (Gardner 2006) summmarise the progress in the area up until 1985 and then 2006.


Brown, Robert G. 1956. “Exponential Smoothing for predicting demand.” Cambridge 42, Massachusetts: Arthur D. Little, Inc.

Gardner, Everette S. 1985. “Exponential smoothing: The state of the art.” Journal of Forecasting 4 (1): 1–28. doi:10.1002/for.3980040103.

Gardner, Everette S. 2006. “Exponential smoothing: The state of the art-Part II.” International Journal of Forecasting 22 (4): 637–66. doi:10.1016/j.ijforecast.2006.03.005.