I have one dependent variable (water consumption) and one independent variable (rainfall). The water consumption variable is non-stationary, so I differenced it to make it stationary. Meanwhile, rainfall is already stationary in nature, so I do not need to difference it.

My question is: since the autoregressive distributed lag (ADL) model includes lagged variable, do I need to difference rainfall variable in order to use the model?

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#### Best Answer

sometimes y is relatable to x and the lags of x . sometimes differences in y are relatable to x and its lags. The whole idea is to determine which and what the order of the differencing is . I suggest you use the procedures of Transfer Function Identification https://onlinecourses.science.psu.edu/stat510/node/75 using possibly different differencing operators in order to pursue a reasonable model.

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