> [!tldr] > > **Box-Cox transformations** are a general class of time series transformations given by $x_{t} \mapsto \begin{cases} > (x_{t}^{\lambda}-1 ) \lambda &\text{if } \lambda \ne 0 \\ \log x_{t} &\text{if } \lambda = 0 > \end{cases}$where $\lambda$ is a parameter. > - The best value of $\lambda$ can either be guessed, or fitted with procedures like maximum likelihood. To select the best $\lambda$, we can look for the one that makes the data the "most Gaussian", in the sense that To select the best $\lambda$, we can look for the one that makes the data the "most Gaussian", in the sense that