How BACK_TRANSFORM, P, B, and LAMBDA Determine Transform Equation - Teradata VantageCloud Lake

Lake - Analyze Your Data with ClearScape Analytics™
Deployment
VantageCloud
Edition
Lake
Product
Teradata VantageCloud Lake
Release Number
Published
February 2025
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en-US
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2026-02-20
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tcl1683670667798

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.

Forward Transform Equations (BACK_TRANSFORM (0))
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
Backward Transform Equations (BACK_TRANSFORM (1))
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)
P, B, and LAMBDA Values of Well Known Forward Transforms (BACK_TRANSFORM (0))
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