Box-Cox transformation

The Box-Cox transformation is a mathematical instrument of regression analysis and time series analysis , with which a stabilization of the variance is to be achieved. The formula is:

${\displaystyle Y_{t}^{(\lambda )}=\left\{{\begin{matrix}{\dfrac {(Y_{t}+c)^{\lambda }-1}{\lambda }}&\quad \mathrm {f{\ddot {u}}r\;\;} \lambda \neq 0\\[10pt]\ln(Y_{t}+c)&\quad \mathrm {f{\ddot {u}}r\;\;} \lambda =0\end{matrix}}\right.}$

There are different methods to find suitable values ​​for . For example, the transformed data can be determined together with other model parameters by means of maximum likelihood estimation or by visual comparison. ${\displaystyle \lambda }$ ${\displaystyle \lambda }$

literature

• George EP Box and David R. Cox: An analysis of transformations . Journal of the Royal Statistical Society Series B 26 (2). 1964. pp. 211-252. JSTOR 2984418