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If I want to run a regression OLS on financial data $y=\beta x + e$ do I need both the $x$ and $y$ to be stationary or is it fine if just the independent variable is stationary? What is usually done in practice?

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  • $\begingroup$ Where is the time index in your model? $\endgroup$ Commented Jan 3, 2017 at 21:38
  • $\begingroup$ Do you mean $x_{t+1}=\beta{x}_t+\epsilon_{t+1}$? $\endgroup$ Commented Jan 4, 2017 at 1:57
  • $\begingroup$ I mean $y_t=\beta x_{t-1}+e_t$ $\endgroup$
    – user25954
    Commented Jan 4, 2017 at 9:01

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In finance many applications call for prediction of future returns based on current or past returns for other vairables. Since these returns are obtained by differentiation all involved variables are stationary.

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From my experience, no not need to make sure $x$ is stationary before fitting an ARIMA model with $y$. Here is a nice post about fitting ARIMA models with regressors: http://robjhyndman.com/hyndsight/arimax/

I found the comments useful as well.

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