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Double exponential smoothing

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The simple exponential forecasting methods like the weighting moving average methods smoothes out data and there is a lag in the forecast relative to the actual data.
If there is a trend in the data, the forecast will be additionally inexact, that’s why the linear trend needs to be integrated in the exponential smoothing model.

A modified version of exponential smoothing exists with a trend adjustment factor (Tn+1):

Where:

  • FTn+1 is the next period forecast taking into account the trend adjustmentFn+1 (Fn) is the next (current) period forecast using simple smoothing method with alpha, see simple exponential smoothing article for full details
  • Tn+1 is  is the exponentially smoothed trend factor for the next period
  • Beta    is the smoothing constant for the trend


Now if Fn+1 is the simple exponential smoothing, then the corrected formula with a trend is the following:



Let’s see what we got using the same data series and taking beta equal to 0.3:



Here Fn is the simple exponential forecast, and TFn is the double exponential forecast taken into account the trend.
We can notice the effect of the trend, where the curve is higher on the index growth and reversely lower in the decrease.

We can also add that there is the same method for seasonal variations, that could be integrated as well in the exponential smoothing model, but better to use a software to “play” with it!

Last modified on Friday, 11 May 2012 08:14

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