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In an ADL model, in order to be consistent do we require both the IV and DV to be stationary? In particular in a process of the form: $$\Phi(L)y_t=\Theta(L)x_t+\epsilon_t$$ where $\Phi(L)$ and $\Theta(L)$ are lag polinomials, do they both have to have roots outside the unit circle or is $\Phi(L)$ having unit roots outside the unit circle a sufficient condition for consistency of OLS estimation?

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    $\begingroup$ Hi Lorenzo. Yes. See section 6 at this link. They usually refer to the $x$ condition as stationarity since roots usually refer to the response. But stationarity and root restrictions I think are equivalent. Also, I always forget but I think, depending on notation, roots for $x$ might need to be inside unit circle. pdfs.semanticscholar.org/fa3a/… $\endgroup$
    – mlofton
    May 5, 2019 at 23:16

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