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