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If x’ and y’ are two first differenced time series, I’ve see many analyses where people find a model where y’ is predicted using x’ in some way (lagged or not).

If both x’ and y’ are stationary with no significant autocorrelation, then is finding a model predicting y’ with x’ a silly thing to do? I don’t think I understand here.

Richard Hardy
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user10136297
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    If both $x’$ and $y’$ are stationary with no significant autocorrelation, then it is more likely that any substantial correlation between them (lagged or not) is in some sense meaningful than correlation between $x$ and $y$ would be, since the latter might more easily be spurious – Henry Dec 11 '21 at 22:44
  • Thank you. Can you also confirm that the beta coefficient we get using the differenced data can be “interpreted” the same way a coefficient is interpreted when regression is done in levels? I have been told different things by about 7 people now, and there is no literature on this that I can find. It’s driving me insane. – user10136297 Dec 11 '21 at 23:23
  • It seems rather clear to me that if we arrive at coefficient B by regressing x’ and y’, then by simply solving your regression equation for y, you easily see that B also describes the relationship between x and y. Therefore the B we get from x’ and y’ can be interpreted using the original data x and y. – user10136297 Dec 11 '21 at 23:35
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    Related: ["Can I use all estimates in a first differenced regression to apply to levels?"](https://stats.stackexchange.com/questions/555684). – Richard Hardy Dec 13 '21 at 18:16

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