Exponential Smoothing


Exponential smoothing of data

The exponential smoothing technique may be used for making a prediction of the next value in a set of data, particularly when this is unknown due to being in the future. For example if the average quantity of a product sold is known for each month of a year then we can then use this information to predict sales for a subsequent month. This adjustment technique uses calculation of weighted averages to provide forecast values which are exponentially weighted equivalents of the original data. Exponential smoothing, as a weighted moving average technique, places more emphasis on the observations which are nearest to the time period being forecast than does simple moving average calculations which weight all original data elements equally.

Related tool:


Moving average calculations.

Script operation

This tool operates in much the same way as most of the others. However, only one column of data may be entered in the input range. A further requestor will also demand the smoothing constant to be used (default is 0.3) which may range from 0 to 1.

As an added feature, the script will present yet another requester that asks whether you wish to enter a starting value for the forecast or use the first actual value in the input range. If you enter 0 (the default), the first actual value will be used.

Click here for information about general script usage.

Typical input data and output information is shown below. Note that any title in the data column may be included within the output by inclusion within the input range.

 
Raw data:       Spreadsheet output:

 Sample 1		Exponential Smoothing	
1			
3		Sample_1	
6		Forecast Values	Standard Error
8		1		0
3		1		1.4142
8		2.4		2.3777
9		4.92		2.5713
7		7.076		2.9346
3		4.2228		3.091
8		6.8668		2.9732
9		8.3601		2.8224
12		7.408		3.0397
14		4.3224		3.1094
15		6.8967		3.0318
		8.369		3.0861
		10.9107		3.0864
		13.0732		3.0184
			
			
		Smoothing	
		Constant=	0.7

Interpretation

The formula used to determine the forecast is:

F(t+1)=F(t)+sc[Y(t)-F(t)]

where:


F(t+1) is the forecast for the next period
F(t) is the forecast for the most recent period
sc is the smoothing constant (1>=sc>=0)
Y(t) is the actual value for the most recent period

In theory, the value of sc is calculated by dividing 1 by the number of actual data points. Here, however, we have chosen to use an sc value of 0.7, which means we value the most recent values more and they will therefore be weighted more heavily in the forecast.

In this example, we have also elected to use the first actual value of the input range to start the forecast series ie. we left the default at 0.

The standard error of each forecast is given in the output - this expresses the variability in the forecast values.



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