The first two tables show how the combined values of BACK_TRANSFORM, P, B, and LAMBDA determine the equation the function uses to transforms the input time series. If a value combination is not in either table, it is disallowed.
The third table shows the P, B, and LAMBDA values of well known forward transforms.
| P | B | LAMBDA | Transform Equation: Wt = |
|---|---|---|---|
| Negative | 0 | 0 | -Ytp |
| 0 | 0 | 0 | ln(Yt) |
| 0 | Positive | 0 | logb(Yt) |
| 0 | 0 | Nonzero | (Ytlambda - 1)/lambda (Box–Cox transform) |
| Positive | 0 | 0 | Ytp |
| P | B | LAMBDA | Transform Equation: Xt = |
|---|---|---|---|
| Negative | 0 | 0 | (-Wt)1/p |
| 0 | 0 | 0 | exp(Wt) |
| 0 | Positive | 0 | bWt |
| Positive | 0 | 0 | (Wt)1/p |
| Positive | 0 | Nonzero | (lambdaWt + 1)1/lambda (Box–Cox back transform) |
| Transform | P | B | LAMBDA |
|---|---|---|---|
| Square root | 1/2 | 0 | 0 |
| Cube root | 1/3 | 0 | 0 |
| Natural log | 0 | 0 | 0 |
| Negative reciprocal | -1 | 0 | 0 |