APO DP – Forecast Model Parameters: Second-Order Exponential Smoothing (Holt and Winter’s)
This document reviews the impact of the parameter Gamma (seasonality) of the Second-Order Exponential Smoothing. The explanation follows a graphical approach without going into the heavy mathematics behind them.
The Second-Order Exponential Smoothing Model (knows as Holt and Winter’s or Holt’s Winter) uses the 3 parameters: Alpha, Beta and Gamma.
- The parameter Alpha (basic value) was introduced in this document:
- The parameter Beta (trend) was introduced in this document:
1. Model Selection: Sales pattern
If you want to select a model manually, then you must analyze the historical data to determine whether a distinct pattern exists according to which you can manually select a model for the system.
If your historical data represents a suspected trend and seasonal behavior, you can select the second-order exponential smoothing. Several methods were devised under the name “double exponential smoothing”. Here we are going to see one method, sometimes referred to as “Holt-Winters double exponential smoothing”.
Suppose that you have the following sales pattern, the Constant Model is clearly not appropriate here:
a = 0.3 -> (MAPE = 17.12)
The Holt Model (Second-Order smoothing with trend and without seasonality) it is more appropriate, but it is still not the best option:
a = 0.3 / b = 0.3 -> (MAPE = 15.37)
Clearly, this linear Extrapolation does not seem appropriate here. These data clearly show seasonal effects
As you can see in the graph below, the seasonal pattern is well extrapolated into the future:
a = 0.3 / b = 0.3 / g = 0.3 -> (MAPE = 14.18)
2. Forecast Model Parameters: Second-Order Exponential Smoothing – Holt and Winters’ Model
There are different methods of 2nd order exponential smoothing models with seasonal pattern and trend pattern. Here we are working with Holt and Winters’ Model.
The system uses the alpha factor for smoothing the basic value. If you do not specify an alpha factor, the system will automatically use the alpha factor 0.3.
The system uses the beta factor for smoothing the trend.
The system uses the gamma factor for smoothing the seasonality.
The following table shows that in this case, there are no variances in the MAPE when the Gamma factor is modified:
Important point for Seasonal Trend models:
Do not use Seasonal Trend method in an automatic fashion: the parameters might need to be tailored to each specific group, especially with large history fluctuations and seasonal peaks and troughs that can be in different months each year!