Exponential Smoothing

Building a best-fit exponential smoothing model involves determining the model type (whether the model needs to include trend, seasonality, or both) and then obtaining the best-fit parameters for the chosen model.

The plot of men's clothing sales over time suggested a model with both a linear trend component and a multiplicative seasonality component. This implies a Winters' model. First, however, we will explore a simple model (no trend and no seasonality) and then a Holt's model (incorporates linear trend but no seasonality). This will give you practice in identifying when a model is not a good fit to the data, an essential skill in successful model building.

Figure 1. Specifying exponential smoothing
Specifying exponential smoothing

We'll start with a simple exponential smoothing model.

  1. Add a Time Series node to the stream and attach it to the source node.
  2. On the Data Specifications tab, in the Observations pane, select date as the Date/time field.
  3. Select Months as the Time interval.
    Figure 2. Setting the time interval
    Setting the time interval
  4. On the Build Options tab, in the General pane, set Method to Exponential Smoothing.
  5. Set Model Type to Simple.
    Figure 3. Setting the model building method
    Setting the model building method
  6. Click Run to create the model nugget.
    Figure 4. Plotting the Time Series model
    Plotting the Time Series model
  7. Attach a Time Plot node to the model nugget.
  8. On the Plot tab, add men and $TS-men to the Series list.
  9. Set the X axis label to Custom, and select date.
  10. Clear the Display series in separate panels and Normalize check boxes.
  11. Click Run.
    Figure 5. Simple exponential smoothing model
    Simple exponential smoothing model

    The men plot represents the actual data, while $TS-men denotes the time series model.

    Although the simple model does, in fact, exhibit a gradual (and rather ponderous) upward trend, it takes no account of seasonality. You can safely reject this model.

  12. Click OK to close the time plot window.
    Figure 6. Selecting Holt's model
    Selecting Holt's model

    Let's try Holt's linear model. This should at least model the trend better than the simple model, although it too is unlikely to capture the seasonality.

  13. Reopen the Time Series node.
  14. On the Build Options tab, in the General pane, with Exponential Smoothing still selected as the Method, select Holts linear trend as the Model Type.
  15. Click Run to re-create the model nugget.
  16. Re-open the Time Plot node and click Run.
    Figure 7. Holt's linear trend model
    Holt's linear trend model

    Holt's model displays a smoother upward trend than the simple model but it still takes no account of the seasonality, so you can discard this one too.

  17. Close the time plot window.

    You may recall that the initial plot of men's clothing sales over time suggested a model incorporating a linear trend and multiplicative seasonality. A more suitable candidate, therefore, might be Winters' model.

    Figure 8. Selecting Winters' model
    Selecting Winters' model
  18. Reopen the Time Series node.
  19. On the Build Options tab, in the General pane, with Exponential Smoothing still selected as the Method, select Winters' multiplicative as the Model Type.
  20. Click Run to re-create the model nugget.
  21. Open the Time Plot node and click Run.
Figure 9. Winters' multiplicative model
Winters' multiplicative model

This looks better; the model reflects both the trend and the seasonality of the data.

The dataset covers a period of 10 years and includes 10 seasonal peaks occurring in December of each year. The 10 peaks present in the predicted results match up well with the 10 annual peaks in the real data.

However, the results also underscore the limitations of the Exponential Smoothing procedure. Looking at both the upward and downward spikes, there is significant structure that is not accounted for.

If you are primarily interested in modeling a long-term trend with seasonal variation, then exponential smoothing may be a good choice. To model a more complex structure such as this one, we need to consider using the ARIMA procedure.

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