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Suppose we have three variables $y_t$, $x_{1t}$, $x_{2t}$. $y_t$ and $x_{1t}$ are co-integrated. $x_{2t}$ is stationary. Now, is the regression model $$\Delta y_t = C + \beta_0(y_{t-1}-\alpha x_{1,t-1}-c)+ \beta_1\Delta x_{1t} + \beta_2 x_{2t}+\epsilon_t$$ valid?

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