I am trying to understand the Vector Error Correction (VEC) Model properly. I have been trying to read from several sites, went through the Chapter in Chris Brooks. But with different sources, the notations change and rather than finding my answers, I get more confused. I request guidance from the stackexchange community.

Let $Y_t, t=1,\ldots,T$, be a $p$-dimensional $I(1)$ time series. Then the VEC model is

$\Delta Y_t=\alpha\beta'Y_{t-1}+\sum\limits_{i=1}^{k}\Gamma_i\Delta Y_{t-i}+\varepsilon_t $

Now, we take $p=2$( i.e., $Y_t= \begin{bmatrix} y_{1t} & y_{2t} \\ \end{bmatrix} $) and assume $r=1$ (cointegration rank) and $k=1$ lag.

Then, $\alpha= \begin{bmatrix} \alpha_1 \\ \alpha_2 \\ \end{bmatrix} $, $\beta'= \begin{bmatrix} \beta_1 & \beta_2 \\ \end{bmatrix} $, $ \Gamma_1= \begin{bmatrix} \gamma_{11} & \gamma_{12} \\ \gamma_{21} & \gamma_{22} \\ \end{bmatrix} $

The dataset is time series with two variables: (natural) log prices of stock and futures. Based on this, I have the following query :

How large or small can the values of $\alpha$ be in ? Most estimations return values $\in(0,-1)$, but I have seen values as low as -4 (with standard error of about 7). Does this indicate mis-specification ?

Re-Edit: Removed two questions.

  • $\begingroup$ First you specify $Y_t$ is $p$-dimensional but then you use $p$ to denote the number of cointegrating relationships. This is a little confusing. Could you use different letters? In addition, I think there are too many questions for a single post. Consider splitting them up individually or in groups of related questions. $\endgroup$ Sep 18 '19 at 16:12
  • $\begingroup$ Hello Sir .. $p$ denotes the count of variables .. sorry for any confusion $\endgroup$
    – square_one
    Sep 18 '19 at 16:14
  • $\begingroup$ Regarding the sign of $\alpha$, check out this thread. $\endgroup$ Sep 18 '19 at 16:14
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    $\begingroup$ Thank you for updating your post. I still think the three questions that you kept are all pretty distinct and deserve to be posted separately. (As for additional motivation: if you care about reputation points at all, more questions means more voting opportunities. This is of course just a side note; the main argument remains the distinctiveness of the questions.) $\endgroup$ Sep 19 '19 at 10:44
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    $\begingroup$ By the way, you may well post multiple questions on separate threads without waiting for the first one to get answered. Just go ahead. $\endgroup$ Sep 19 '19 at 19:37

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