You might want to read Guerrero, V.M. (1993) Time-series analysis supported by power transformations. Journal of Forecasting, 12, 37–48.

The above paper is the only one that I know of have developed automatic technique to determine  box cox transformation parameter lambda. This is implemented in the $forecast$ package in $R$ software. See example below:

$$Library('forecast')$$
$$lambda <- BoxCox.lambda(AirPassengers,lower=0)$$