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This question came up in learning autoregressive distributed lag models [ARDL]. Say you have a dependent variable which needs to be differenced once to be stationary. And you have predictors some of which are already stationary, some of which need to be differenced once to be stationary, and some that need to be differenced twice to be so.

Can you difference them all to be stationary and analyze the resulting regression? I ask this because I have run into comments in various places that say variables can not be integrated of a different order - and I am not sure what that really means.

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Differencing can differ ... see here and here and here and Transfer function in forecasting models - interpretation.

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