The data are heteroscedastic and non-stationary. Differencing it may make it stationary and/or homoscedastic to meet the assumptions for VAR and/or ARDL applications.

Thanks Etta for your answer but An ARDL model has been simplified so that all variables are 1(0) and differencing is no longer necessary, however, non-spherical errors are present and one of the variables needs to be instrumented.

Did you try Mahalanobis distance?

Thank you but I do not believe Mahalanonis D squared can be helpful here since we are not interested in adjustment of statistical distance of the regular Euclidean distance to handle covariance matrices that are not scalar only, My application is more to time series.

Sorry for late reaction, missed reply from 27th of February. Mahalanobis distance is a way to make such a transformation of the initial data space, that distance in transformed space becomes Euclidean. It does not imply that data are time series or not. It's about proper handling of correlated and heteroscedastic errors.