# VECM with first differences? [closed]

Is it ok to take first differences of data which is non stationary in levels but stationary in first differences (and cointegrated), and input these differenced variables into the VECM? Or does this constitute over differencing given th VECM differences the data as well?

• If your variables are cointegrated then you don't need to difference them. That's the whole point of cointegration. Sep 11 '19 at 5:05
• Is it ok to difference them again though? as this provides better results in my Impulse Response Functions Sep 11 '19 at 5:56
• Possible duplicate of Levels or First Differences, VECM or VAR for Ultimate Impulse Response Functions? Sep 11 '19 at 7:31

When the variables are integrated of order one, I(1), and cointegrated, VECM is specified with variables in differences on the left hand side of the equation: $$\Delta y_t=\Pi y_{t-1}+\Gamma_1\Delta y_{t-1}+...+\Gamma_{p-1}\Delta y_{t-(p-1)}+\varepsilon_t.$$ The right-hand-side variables are all differenced except for the error correction term which is a linear combination (or several of them) of $$y_{t-1}$$ in levels.
If you specify a VECM of the form $$\Delta^2 y_t=\Pi\Delta y_{t-1}+\Gamma_1\Delta^2 y_{t-1}+...+\Gamma_{p-1}\Delta^2 y_{t-(p-1)}+u_t$$ instead, you have overdifferencing your series, and that is a problem.