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I have some response variable $Y$ that I am trying to model with OLS. There is a single independent variable $X_{t,N}=Y_t-Y_{t-N}$ for some $N$. However, when I do such a simple regression, I obtain that my errors are auto-correlated. Irrespective of the lag, $N$, that I use. The data itself, is autocorrelated. I have been looking a lot, and things like ARIMA, VAR, etc. come up. But I don't think they are useful in my case because I am not predicting $Y$ with its lagged values, but rather with its differenced values. Single response, single independent variable. How does one treat autocorrelation in the independent variable like here?

Additional question, is how to then add more lags: $Y_{t+1} = c + b_0*X_{t,N} + b_1*X_{t,(N-5)}+b_2*X_{t,(N-10)}$. Now they are autocorrelated + correlated...

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