# Queries on Interpretation of Vector Error Correction Model

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.

• 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. Sep 18 '19 at 16:12
• Hello Sir .. $p$ denotes the count of variables .. sorry for any confusion Sep 18 '19 at 16:14
• Regarding the sign of $\alpha$, check out this thread. Sep 18 '19 at 16:14
• 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.) Sep 19 '19 at 10:44
• By the way, you may well post multiple questions on separate threads without waiting for the first one to get answered. Just go ahead. Sep 19 '19 at 19:37