A transformation is a change of scale applied to each observation, such as taking logarithms, so that variation or shape becomes easier to study. An adjustment is a change made to correct or simplify a feature of the series, such as removing a changing level, handling a calendar effect, or treating an unusual observation.
A transformation is a change of scale applied to each observation, such as taking logarithms, so that variation or shape becomes easier to study. An adjustment is a change made to correct or simplify a feature of the series, such as removing a changing level, handling a calendar effect, or treating an unusual observation.
If monthly sales grow and the ups and downs become larger as the level rises, a logarithmic transformation can make the variation more stable before further analysis.
Transformations should be chosen from the nature of the data, not from habit. If variability is already stable, transforming without reason can make interpretation harder.
Each positive value Y is replaced by log(Y). Percentage-like growth and increasing spread often look more regular after a log. Values must be positive. After analysis, results may need to be converted back to the original units for a practical report.
Each non-negative value Y is replaced by √Y. This is a milder change than a logarithm and is sometimes used when counts are moderately variable. It is not required for every series.
Differencing replaces a series by its period-to-period changes: Dt = Yt − Yt−1. This can remove a steadily changing level so that the remaining series is easier to look at. Unit 2 only needs this idea. Detailed use of differencing inside ARIMA models belongs to Unit 3 and is not developed here.
Sales 40, 42, 45 have first differences 2 and 3. The original series is climbing; the differences describe the size of each step.
| Transformation | Adjustment | |
|---|---|---|
| Main idea | Change the scale of the values | Correct or simplify a feature of the series |
| Typical tools | Log, square root | Differencing, calendar correction, treating an outlier |
| Simple example | log of monthly sales | First difference of a climbing series |
Suppose weekly sales rise and the later weeks bounce more than the early weeks. A time plot of the raw series would show a widening fan. A plot of log sales may look more even. That does not prove a model; it only shows why a transformation might be considered. If instead the problem is a steadily rising level with similar bounce, a difference of the original series may be the more relevant adjustment.