# Box-Cox Transformation¶

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 $$N$$ None

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 None
$$\lambda$$ $$\lambda \in \mathbb R$$ None Estimated transformation parameter In some cases, it may be given by the user as an input parameter

Single Steps using the Algorithm

References