SARIMAX: transforming the exogenous variables

External question — Cross Validated Stack Exchange Author: Nick Original post: https://stats.stackexchange.com/questions/441812 License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/ Adaptation: HTML converted to plain text; contact email addresses removed. I am trying to build a (S)ARIMAX model where the endogenous variable (daily stock log-returns) has already been transformed: the log returns are the first difference of the logs of the daily stock price. This should make the time series of the endogenous variable roughly stationary. Does it mean that I need to similarly transform the exogenous variable (daily trade volume)? The exogenous variable is on a different scale - it denotes counts of shares (i.e. integer-valued and well above 10^8) rather than price (a float smaller than 200) and exhibits a different pattern - for the observed period the trade volume drops while the stock price increases.

External answer — Cross Validated Stack Exchange Author: IrishStat Original post: https://stats.stackexchange.com/a/441813 License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/ Adaptation: HTML converted to plain text; contact email addresses removed. I would work with the original (observed) data ( properly scaled to be commensurate) and after having treated/detected anomalies via Intervention Detection and evolved a possible representation (SARIMAX) including the latent deterministic structure ... I would consider examining the residuals to ascertain whether there was a systematic behavior between the level of the series and the error variance or whether GLS was more appropriate. This thread Incorrect Lambda value with Box-Cox transformation on time series data in python might help further

External answer — Cross Validated Stack Exchange Author: MasterPuri Original post: https://stats.stackexchange.com/a/441831 License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/ Adaptation: HTML converted to plain text; contact email addresses removed. You could difference the exogenous variable and then go from there, however, you don't necessarily have to. For example, you could model daily log stock returns with the daily trade volume of the previous day.