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I am currently looking at long-horizon regressions, to be clear,

$$Y_{t,k}=\theta X_{t-1}+ε_t$$

Where, the dependent variable is a k-period return, regressed on a lagged predictor.

I have seen many examples in the literature where $X$ is a persistent variable.

Can anyone provide an example of when this could be useful if $X$ is stationarity and not very persistent?

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