The Newey-West HAC standard errors that accommodate both AutoCorrelation and Heteroskedasticity might be worth considering.

The Box-Cox model tries to accommodate heteroskesdasticity under normality, or normality under heteroskedasticity.

The log and sqrt models are special cases of Box-Cox, so normality should be checked.

Hiba Abi Hussein, if you say what software you are using, someone may be able to give better advice about how to estimate a model that allows for heteroscedasticity.

Thank you for your help. Much appreciated!

Bruce Weaver I am using R software.

I have other measurements. when I include them in the model, at some point the heteroscedasticity is somehow reduced but not totally surpassed.

I suggest to look at this paper: "Dynamic Modulus Model of Hot Mix Asphalt: Statistical Analysis Using Joint Estimation and Mixed Effects", by José Pablo Corrales-Azofeifa and Adrián Ricardo Archilla published in the ASCE Journal of Infrastructure Systems, 2018, 24(3). It may be way out of your field but in that paper we did something similar to what you described to account for different variance structures of different data sets. We also used R, but we used non-linear models.

I suggest that you model the within -subject heteroscedasticty as a function of relevant variables - these could be either continuous or categorical (eg gender) or indeed time.

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