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Exponential smoothing

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Let’s now dig into the most popular forecasting methods: the simple exponential smoothing model to forecast the next period for a time series without trend, and the double exponential smoothing model taking into account a trend effect.

Single exponential smoothing

The single exponential smoothing is somewhat similar to the moving average methods except that there is a single weighting factor called alpha, which can take a value between 0 and 1.
The next period forecast (Fn+1 ) is then calculated as following:


  • Fn is the current period forecast
  • Alpha is the smoothing factor
  • An is the actual sales for the current period

If  alpha is near 0, then the next period forecast is equal to the previous forecast, which means that the model is less reactive.
On the opposite, if alpha is near 1, the next period forecast is equal to the previous period actual sales, meaning that now the model is over reactive.

In summary, the reactivity of the model depends on alpha: when close to 1, the model is very reactive and the latest periods are more important and when alpha is close to 0, the model is less reactive so former periods are more important.

Tip: When  alpha = 2 / (N+1) with N is the number of periods, we get the straight moving average!

How to determine the smoothing factor (alpha)

You can determine alpha either on an empiric or scientific way. Its value allows to fine tune the model sensitivity.

The empiric way basically is you in front of your computer “playing with the model” till it fits the actual sales based on historical data. This way you get your “golden number” for alpha.
The scientific method is using the standard error method for estimating alpha.

Let’s take the Dow Jones index to see the results with 2 alpha values:

We can notice that the green curve with alpha equal to 0.2 is certainly not precise, and the purple curve with alpha equal to 0.9 looks much better.

Having done the standard error method, it has confirmed that 0.9 is the best value for alpha to fit this very instable data.

You can also see that the forecast data lag the actual data in the model whatever value for alpha.

Last modified on Wednesday, 29 August 2012 15:01

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