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