The Simple Smoothing Average Specification window appears when you select Simple Moving Average as the smoothing model. Let w be the smoothing window width in a simple moving average (SMA) model. Let ft=(yt+yt-1+yt-2+...yt-(w-2)+yt-(w-1))/w be the average of w consecutive observations for some time point t.
Figure 15.9 Simple Smoothing Average Specification Window
The smoothing window width, w, that defines the number of consecutive points to average. The larger the window width, the more the series is smoothed.
The smoothing window is constructed from the points leading up to and including the time point, t, the point at which the series is being estimated. In other words, ft is the plotted value for time t.
|
–
|
|
–
|
For even w, ft is the plotted value for time t-(w-1)/2. When saved to a data table, ft is at t-(w-2)/2.
|
For even w, the smoothing window cannot be centered around the time point at which the series is being estimated. This option creates two smoothing windows that are almost centered, and averages them together. The smoothing estimates are calculated as follows:
Figure 15.10 Smoothing Model Specification Window
Expands the dialog to enable you to set constraints on individual smoothing weights. Each smoothing weight can be Bounded, Fixed, or Unconstrained as determined by the setting of the popup menu next to the weight’s name. When entering values for fixed or bounded weights, the values can be positive or negative real numbers.
Figure 15.11 Custom Smoothing Weights
The example shown in Figure 15.11 has the Level weight (α) fixed at a value of 0.3 and the Trend weight (γ) bounded by 0.1 and 0.8. In this case, the value of the Trend weight is allowed to move within the range 0.1 to 0.8 while the Level weight is held constant at 0.3. Note that you can specify all the smoothing weights in advance by using these custom constraints. In that case, none of the weights would be estimated from the data although forecasts and residuals would still be computed.