Transformations of Variables - Smoothing Tab
Select the Smoothing tab of the Transformations of Variables dialog box to access the options described here. The general purpose of smoothing techniques is to "bring out" the major patterns or trends in a time series, while de-emphasizing minor fluctuations (random noise). Visually, as a result of smoothing, a jagged line pattern should be transformed into a smooth curve.
| Element Name | Description |
|---|---|
| OK (Transform selected series) | Click the OK (Transform selected series) button to transform the selected variable (series) and display a plot of the analysis. Transformed variables are appended to the active work area. If a transformation produces an invalid value (e.g., square root of a negative value, division by zero, etc.), STATISTICA assigns a missing data value; then, in a second pass, those missing data are replaced according to your selection on the Time Series Analysis Startup Panel - Missing Data tab. |
| Transformation | Use the options in the Transformation group box to select the desired type of transformation. |
| N-pts mov. averg. | If you select the N-pts mov. averg option button, each point in the transformed series is computed as the mean of N points (where N is the value entered in the adjacent N= box), the so-called moving average window. If the N parameter is odd, then the moving average is naturally centered in the middle of the moving average window. If N is even, the moving average is centered by averaging each pair of uncentered means. |
| Prior | If the Prior check box is selected, then the moving average is computed from the N preceding values. |
| Weighted | If the Weighted check box is selected, then a weighted moving average is computed. Click the Specify Weights button to display the Specify the moving average weights dialog box in order to specify the respective weights. |
| N-pts mov. median. | If the you select the N-pts mov. median option button, each point in the transformed series is computed as the median of N points (where N is the value entered in the adjacent N= box). If the N parameter is odd, then the moving median is naturally centered in the middle of the moving median window. If N is even, the moving median is centered by averaging each pair of uncentered medians. |
| Prior | If the Prior check box is selected, then the moving median is computed from the N preceding values. |
| Simple exponential | If you select the Simple exponential option button, each point is computed as a weighted average of all preceding observations, where greater weight is assigned to more recent observations (specifically, the weights decrease geometrically with the "age" of prior observations). Algorithmically, this is accomplished by:
St = α*Xt+(1-α)*St-1 where St is the value of the transformed series at time t, St-1 is the value of the transformed series at time t-1, Xt is the value of the untransformed series at time t, and α (Alpha) is a constant (0<α<1). If α is close to 0 (zero), then more emphasis is placed on (greater weight is assigned to) observations prior to a particular time t, resulting in a smoother curve; if α is close to 1, then more emphasis is placed on the respective untransformed observation at time t, resulting in a curve that is less smooth, but more closely following the actual (untransformed) data. Note that a complete implementation of exponential smoothing and forecasting is also available from the Startup Panel. See also Exponential Smoothing. |
| 4253H Filter | This transformation consists of several passes of moving average/median smoothing, and is a powerful filter for smoothing a series. If you select the 4253H Filter option button, the following transformations are performed: (1) a 4 points moving median centered by a moving median of 2, (2) a 5 point moving median, (3) a 3 point moving median, and (4) a 3-point weighted moving average using Hanning weights (.25, .5, .25), (5) residuals are computed by subtracting the transformed series from the original series, (6) steps 1 through 4 are then repeated for the residuals, (7) the transformed residuals are added to the transformed series. In practice, this filtering method often produces a smooth series while maintaining the salient characteristics of the original series. |