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?

  • $\begingroup$ You did the right thing by taking the first difference. This avoids spurious regression in your ADL model. $\endgroup$ Jan 9, 2016 at 17:59
  • $\begingroup$ You don't have to difference rainfall. $\endgroup$ Jan 9, 2016 at 18:02
  • $\begingroup$ People are talking about climate change. So rainfall is becoming more extreme and this means higher variance in recent years. Is it still a good idea to assume rainfall stationary? $\endgroup$
    – Ken T
    Apr 11, 2018 at 16:07

2 Answers 2


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://web.archive.org/web/20151025004937/https://onlinecourses.science.psu.edu/stat510/node/75 using possibly different differencing operators in order to pursue a reasonable model.


You do not need to difference data in order to utilize an autoregressive distributed lag model (ADL). An ADL model implies that lagged variables of the dependent and independent variable are included as explanatory variables in the specification.


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