This example illustrates how to use XLMiner's Double Exponential Smoothing technique to uncover trends in a time series that contains seasonality. On the XLMiner ribbon, from the Applying Your Model tab, select Help - Examples, then Forecasting/Data Mining Examples, and open the example data set, Airpass.xlsx. This data set contains the monthly totals of international airline passengers from 1949-1960. After the example data set opens, click a cell in the data set, then select from the Time Series tab, select Partition to open the Time Series Partition Data dialog.

Select Month as the Time Variable, and Passengers as the Variables in the Partition Data.

Time Series Partition Dialog 

Click OK to partition the data into Training and Validation Sets. The Data_PartitionTS worksheet is inserted to the right of the Data worksheet.

Click the Data_PartitionTS worksheet, then on the XLMiner ribbon, from the Time Series tab, select Smoothing - Double Exponential to open the Double Exponential Smoothing dialog.

Month is already selected as the Time variable. Select Passengers as the Selected variable, then under Output Options, select Produce Forecast on validation to test the forecast on the Validation Set.

This example uses the defaults for both the alpha and trend parameters. XLMiner includes a feature that chooses the alpha and trend parameter values that result in the minimum residual mean squared error. It is recommended that this feature be used carefully, as this feature most often leads to a model that is overfit to the Training Set. An overfit model rarely exhibits high predictive accuracy in the Validation Set.

Double Exponential Smoothing Dialog 

Click OK to run the Double Exponential Smoothing algorithm. Two worksheets, DoubleExponentialOutput and DoubleExponential_Stored, are inserted to the right of the Data_PartitionTS worksheet.

Click on the DoubleExponentialOutput worksheet to view the results of the smoothing. When comparing the outputs of Exponential and Moving Average Smoothing, Double Exponential Smoothing results in a better fit when used with a data set including seasonality (Training Set MSE = 876.05, and Validation Set MSE = 8043.08).

If the Optimize algorithm is used, an Alpha of .9568 is chosen along with a Trend of 0.009.

Double Exponential Time Plot of Actual Vs. Forecast Training Data   

Double Exponential Smoothing Error Measures (Training Data)

Double Exponential Time Plot of Actual Vs Forecast Validation Data

Double Exponential Smoothing Error Measures (Validation Data)

 

Double Exponential Smoothing Dialog 

 

 Double Exponential Smoothing Output:  Inputs

The displayed parameters result in an MSE of 450.7 for the Training Set, and an MSE of 8477.64 for the Validation Set. Again the model created with the parameters from the Optimize algorithm resulted in a model with a better fit than a model created with the default parameters.

Double Exponential Smoothing Output:  Time Plot of Actual Vs Forecast (Training Data)   

Double Exponential Output Error Measures (Training)

Double Exponential Smoothing Output:  Time Plot of Actual Vs Forecast (Validation Data)

Double Exponential Smoothing Output:  Error Measures (Validation)