Different Exponential Smoothing Models for Forecasting
There are many different exponential smoothing methods have been introduced, such as Brown's Double Exponential Smoothing, Holt's Two-Parameter Trend Model and Winters' Three-Parameter Exponential Smoothing. In this tutorial, we would use the EVIEWS to demonstrate and generate three similar exponential smoothing forecasts for the same sample data from the textbook. Will we get a better result? And which one is the best forecasting model?
Here are the steps to follow the demonstration, after seeing it, you will get some ideas to answer the above questions.
Firstly, prepare an Excel data file to contain the following time series data (Table 6-8 in textbook): Excel file
Secondly, use the Excel file to create the following "Workfile" in EVIEWS:
Double click the time series "demand" and get the following window:
Then choose "Proc", "Exponential Smoothing" to get the preset dialogue box as following:
Now, you are ready to generate a forecast series by using different models.
1. Brown's Double Exponential Smoothing Model:
In the exponential smoothing dialogue box, choose "Double" for "Smoothing Method", specify the values of the "Smoothing Parameters" and type "0.15" for "Alpha" (same as the optimum alpha which is given by Table 6-8, pp.220), provide a name as 'DEMANDSM1" for the "Smoothed Series", specify the "Estimation Sample" period upon which to base the forecasts and type "2 30" (in order to compare the RSE of Table 6-8 to the results from EVIEWS), then specify the sample period upon which to base your forecasts change " Circle for Seasonal" from "5" to "0", because there is no cycle for seasonal. The output is as following:
After clicking " OK", the smoothed series "DEMANDSM1" will be generated and appeared in the "workfile", meanwhile also get the statistics result as following:
As we can see the RMSE is 6.606836 which reflects how best is the fitted model. Whether this is the smallest RMSE, you may try different values of "Alpha" and compare the results from other fitted models.
¡@
2. Holt's Two-Parameter Trend Model:
Choosing "Holt-Winter-No seasonal" for "Smoothing Method", specify the value "0.2" for "Alpha" and "0.6" for "Beta" of "Smoothing Parameters" (arbitrary values can be specified since we don't know the optimum combination for them), provide a name 'DEMANDSM2" for "Smoothing Series", type "2 30" for "Estimation Sample", (as we want to compare the RMSE with the previous Double exponential smoothing model and Table 6-8), then change " Circle for Seasonal" from "5" to "0". The output is as following:
After click "OK" and get":
As we can see, the RMSE (6.836326) from the Holt's Two-Parameter Trend Model is a little bit higher than that RMSE (6.606836) from the Brown's Double Exponential Smoothing Model.
However, we cannot make a decision on which exponential smoothing model is better now since we don't know the optimum combination of alpha and beta for Holt's Two-Parameter Trend Model, this optimum combination can be obtained through many trials and errors so as to get the minimum RMSE. For Example, if you change the alpha and beta value to become 0.1 and 0.7, the RMSE will be 6.331150 which is smaller than the above one (Try it yourself). Base on the minimum RMSE criteria, which model is better than the other depend on which model give you the smaller RMSE.
3. Winters' Three-Parameter Exponential Smoothing Model:
(Students can either choose Holt-Winter-Additive or Multiplicative which depends on data's characteristics)
Choosing "Holt-Winter-Multiplicative" for "Smoothing Method", "0.1" for "Alpha" and "0.1" for "Beta" and "0.1" for " Gamma" of "Smoothing Parameters" (arbitrary values since we don't know the optimum combination for them), name' DEMANDSM3" for "Smoothing Series", type "2 30" for "Estimation Sample", (as we want to compare the RMSE with previous demonstrations and Table 6-8), then change " Circle for Seasonal" from "5" to "0". The output is as following:
After click "OK" and get:
As we can see, the RMSE is 6.249651 from Winters' Three-Parameter Exponential Smoothing Model, which is smaller than the other two above. Of course, there may obtain further smaller RMSE if we had known the optimum combination of "alpha", "beta" and "gamma". However, to know the optimum combination is time consuming by trials and errors of many different combination of three parameters.
To sum up, exponential smoothing forecasting model is performed better under Eviews than under Excel, given the same smoothing parameter (s). Moreover, to obtain a best fitted model, there are no guarantee which exponential smoothing models, until you try enough trails and errors to find the minimizing RMSE and then adopt that best model.
The End
¡@