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I am wondering if someone can help me with explaining some variables in that VECM equation in a matrix form and checking if my previous assumptions are right about the parameters.

  • So $\varphi$ in that equation would be a constant and explain the drift of the time series data.
  • $\alpha$ explains how fast the deviation in the previous periode is corrected.
  • The term after explains how high the deviation from the equilibrium is in the previous period and could be rewritten as $\text{ECT}_{t-1}$ (error correction term).
  • The second last matrix shows the changing in the time series data.
  • Why is there a 2x2 matrix and what is it explaining?
  • In the ECT-term I am wondering what the $\beta_0$ is for, cause I found some books that write it without a constant? enter image description here
Richard Hardy
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Tobias Emil
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    All is fine with your explanation. What 2x2 matrix are you interested in, the one with $\delta$ and $\rho$ term? These are just coefficients in front of the lagged series $\Delta Y_{t-i}$ and $\Delta X_{t-i}$, otherwise these lags would all have coefficient 1 in front of them. $\beta_0$ is needed if the stationary combination of the time series fluctuates around some constant that is not zero. When accounted for that by $\beta_0$, you can interpret negative and positive values of the ECT as negative and positive deviations from the equilibrium. – Richard Hardy May 07 '18 at 17:26
  • Yes, thats exactly what I wanted to now, thanks for the quick answer. – Tobias Emil May 07 '18 at 17:42
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    I have posted my comment as an answer. If it is clear, you may accept it by clicking on the tick mark to the left. This is [how Cross Validated works](https://stats.stackexchange.com/tour). – Richard Hardy Jun 01 '18 at 20:04
  • Just a heads up regarding my last comment. – Richard Hardy Sep 11 '19 at 06:20

1 Answers1

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All is fine with your explanation.

The 2x2 matrix with $\delta$ and $\rho$ terms are coefficients in front of the lagged series $\Delta Y_{t−i}$ and $\Delta X_{t−i}$. Without it, these lags would all have coefficient 1 in front of them.

$\beta_0$ is needed if the stationary combination of the time series fluctuates around some constant that is not zero. When accounted for that by $\beta_0$, you can interpret negative and positive values of the ECT as negative and positive deviations from the equilibrium.

Richard Hardy
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