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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.

square_one
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  • 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. – Richard Hardy Sep 18 '19 at 16:12
  • Hello Sir .. $p$ denotes the count of variables .. sorry for any confusion – square_one Sep 18 '19 at 16:14
  • Regarding the sign of $\alpha$, check out this thread. – Richard Hardy Sep 18 '19 at 16:14
  • I saw your answer on that question. I did not understand it. Wouldn't that make the variable $Y_t$ keep increasing ? Also, In my case of variables (stock and future), can the $\alpha$ be positive or $<-1$? – square_one Sep 18 '19 at 16:20
  • No, it would not make the variable keep increasing. – Richard Hardy Sep 18 '19 at 18:51
  • Request to reopen: Removed extra questions and added more context. – square_one Sep 19 '19 at 10:21
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    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.) – Richard Hardy Sep 19 '19 at 10:44
  • @RichardHardy .. Thank You Sir .. when I tried to raise new individual questions .. I found some existing relevant posts.. it seems that the search function at the "Ask Question" works much better than google :) – square_one Sep 19 '19 at 15:09
  • I am glad to hear that was helpful! Indeed, if you inspect your questions one by one, it will be much easier to locate relevant posts. Perhaps one or two are even duplicates. – Richard Hardy Sep 19 '19 at 16:00
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    By the way, you may well post multiple questions on separate threads without waiting for the first one to get answered. Just go ahead. – Richard Hardy Sep 19 '19 at 19:37
  • Suggestions for further improving the post: 1. The title could be edited to match the specific question 2. Complete reference with book name etc. for "the Chapter in Chris Brooks" – Juho Kokkala Sep 21 '19 at 13:29

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