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When running a time series, the Dickey-Fuller test of the dependent variable is statistically significant, meaning that it is stationary (which is also confirmed by looking at a plot of the variable). However, the independent variables which I'm using to predict the outcome are non-stationary, according to the Dickey-Fuller test.

So my question is: what to do in a time-series regression with a stationary dependent variable and a bunch of non-stationary covariates? To be more precise, I want to use an ECM (Error Correction Model).

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First, you could try power transformations (e.g. log, square root, multiplicative inverse, etc.). To determine which power transformation is best for the non-stationary covariates, you can employ the Box-Cox technique.

If power transformations don't help, check the time series for seasonal trends. If they exist, deflation or seasonal adjustment may be necessary to account for those patterns.

In preparation for time series modeling, consider differencing and detrending. Here's a helpful article: http://www.mathworks.com/help/econ/data-transformations.html

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  • $\begingroup$ I already differentiated the independent variables. Should I also differentiate the dependent variable, even if it is stationary? $\endgroup$
    – Not Fisher
    Commented Apr 14, 2015 at 17:07

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