Box-Cox Transformation

Global Algorithm - One-Dimensional Algorithm

Box-Cox Transformation algorithm is a useful data pre-processing technique. It can be used to make the non-normally distributed data normal and stabilise variance of the time series data that is non-stationary in variance.

Input Parameters

Parameter	Type	Constraint	Description	Remarks
\(Y\)	\(Y \in \mathbb R^N\)	\(N \in \mathbb{N}, Y > 0\)	Input data vector of length \(N\)

Output Parameters

Parameter	Type	Constraint	Description	Remarks
\(\hat{Y}\)	\(\hat{Y} \in \mathbb R^N\)	\(N \in \mathbb{N}\)	Data vector of length \(N\) that has approximately normal distribution
\(\lambda\)	\(\lambda \in \mathbb R\)		Estimated transformation parameter	In some cases, it may be given by the user as an input parameter

Tool Support

• Matlab

  For details refer to the online documentation of the function ‘boxcox’.

Single Steps using the Algorithm

• Reducing Data Nonnormality with Box-Cox Transformation
• Stabilizing Variance with Box-Cox Transformation

References

• R.M. Sakia, The Box-Cox transformation technique: a review, The Statistician, vol. 41, pp. 169-178, 1992.

  http://staff.ustc.edu.cn/~zwp/teach/Reg/Boxcox.pdf