# Box-Cox, Exogenous Variables and Time Series Models

I am building time series models using SARIMAX from Statsmodels (Python).

The independent variables in my models include 3 to 5 exogenous variables that are other than the target variable I am trying to predict.

I am finding that there is some value in using Box-Cox to transform my target (i.e. independent) variable.

In these cases, should I also be applying the same Box-Cox transformation to my exogenous variables?

(I believe the answer is no.)

• Would you be willing to transform some of the variables but not all of them? That is tantamount to using a different transformation (no transformation is the Box-Cox transformation of power $1$).
– whuber
May 6 at 15:46
• Yes - transforming only some of my exogenous variables would be an option. May 6 at 16:11
• Then you have provided the answer.
– whuber
May 6 at 16:14
• Ok, so I think I am hearing the following advice: (1) explore box-cox transforms for each of my exogenous variables, (2) each such transform might use a different lambda value. Am I getting that right? If yes, how would I describe what the benefit of these transforms might be? May 6 at 17:12
• That's a broad question. I have provided some answers at stats.stackexchange.com/a/4833/919 and stats.stackexchange.com/a/35717/919. Also see some of the discussion at the end of stats.stackexchange.com/a/259223/919. Here's an entire thread on understanding Box-Cox transformations: stats.stackexchange.com/questions/467494.
– whuber
May 6 at 17:16