<p>Based on the <a href="https://www.mathworks.com/help/econ/jcitest.html" rel="nofollow noreferrer">official documentation</a>, you have found that there is one cointegration relationship with 95% probability. Given your selection of <code>Model: H1*</code> and <code>Lags: 4</code>, the model you are estimating is:</p>

<p>$$ \Delta y_t = A(B´y_{t−1}+c_0) + B_1\Delta y_{t-1} + B_2\Delta y_{t-2} + B_3\Delta y_{t-3} + B_4\Delta y_{t-4} + \epsilon_t $$</p>

<p>The matrix <code>B</code> is of dimension $n \times r$, and it contains as columns the cointegration vector(s). In your case, $r=1$, and the cointegration vector is</p>

<pre><code>B =
0.7081
1.6282
-2.4581 
</code></pre>

<p>The Matrix <code>A</code> represent the "error-correction" matrix. For a system to converge towards the equilibrium cointegration relation (i.e. to be stable), you want these numbers to be in between -2 and 0 (as in your case).</p>

<p><code>c0</code> is just a constant of the cointegration relationship (like in a standard function $y=c0+bx$).</p>

<p>The matrices <code>Bi</code> show how previous period shocks translate through the system over time.</p>

CC BY-SA 3.0
2017-08-26T10:10:30.570Z
Thank you. What about the other paramters? Reading other posts a value greater than +- 2 is significant. Is this the right assumption?
Adrian
CC BY-SA 3.0
2017-08-26T17:47:57.963Z
@Adrian Can you a bit more specific on which parameters are you refering to? Not sure what you mean.
luchonacho
CC BY-SA 3.0
2017-08-27T09:21:42.060Z
A, B, B1, B2, c0, c1
Adrian
CC BY-SA 3.0
2017-09-01T10:30:12.267Z
@Adrian what do you think of the update? Still got questions?
luchonacho
CC BY-SA 3.0
2017-08-25T18:09:06.723Z
2017-08-29T11:35:57.660Z
2017-08-29T11:35:57.660Z
luchonacho
<p>After testing for cointegration with Johansen test using the following code</p>

<pre><code>[h,pValue,stat,cValue,mles] = jcitest(ret,'model','H1*','lags',4,'display','params')
</code></pre>

<p>I received this output:</p>

<pre><code>Data: prices
Effective sample size: 56
Model: H1*
Lags: 4
Statistic: trace
Significance level: 0.05


r  h  stat      cValue   pValue   eigVal   
----------------------------------------
0  1  40.5214   35.1929  0.0161   0.3350  
1  0  14.6781   20.2619  0.1453   0.1667  
2  0  5.4670    9.1644   0.1580   0.1091 
</code></pre>

<p>So it rejects no cointegration. So I am running the VECM with rank 1 restriction: </p>

<pre><code>B = mles.r1.paramVals.B % Cointegrating relations with rank = 1 restriction
</code></pre>

<p>I get the following output:</p>

<pre><code>r = 1
------
A =
-0.6259
-0.2261
-0.0222

B =
0.7081
1.6282
-2.4581

B1 =
0.0579 1.0824 -0.8718
0.1182 0.4993 -0.5415
0.1050 0.1667 -0.1600

B2 =
-0.5462 2.2436 -1.7723
-0.1518 0.6605 -0.6169
-0.1610 0.5966 -0.5366

c0 =
2.2351

c1 =-0.0366
0.0872
0.1444
</code></pre>

<p>How would I interpret this output and how do I move forward after estimating the parameters? (I have only displayed the r=1, and these are not the actual results, by I couldn't find any explanation behind them) </p>

<econometrics><time-series>
VECM interpretation in Matlab?
Adrian
# VECM interpretation in Matlab?

(Asked by: username_0 on 2017-08-24)

After testing for cointegration with Johansen test using the following code
[h,pValue,stat,cValue,mles] = jcitest(ret,'model','H1*','lags',4,'display','params')

I received this output:
Data: prices
Effective sample size: 56
Model: H1*
Lags: 4
Statistic: trace
Significance level: 0.05


r  h  stat      cValue   pValue   eigVal   
----------------------------------------
0  1  40.5214   35.1929  0.0161   0.3350  
1  0  14.6781   20.2619  0.1453   0.1667  
2  0  5.4670    9.1644   0.1580   0.1091 

So it rejects no cointegration. So I am running the VECM with rank 1 restriction: 
B = mles.r1.paramVals.B % Cointegrating relations with rank = 1 restriction

I get the following output:
r = 1
------
A =
-0.6259
-0.2261
-0.0222

B =
0.7081
1.6282
-2.4581

B1 =
0.0579 1.0824 -0.8718
0.1182 0.4993 -0.5415
0.1050 0.1667 -0.1600

B2 =
-0.5462 2.2436 -1.7723
-0.1518 0.6605 -0.6169
-0.1610 0.5966 -0.5366

c0 =
2.2351

c1 =-0.0366
0.0872
0.1444

How would I interpret this output and how do I move forward after estimating the parameters? (I have only displayed the r=1, and these are not the actual results, by I couldn't find any explanation behind them)

**Tags:** econometrics, time-series

---

## 1 answers

### Answer by username_1 on 2017-08-25. Score: 2

Based on the official documentation, you have found that there is one cointegration relationship with 95% probability. Given your selection of Model: H1* and Lags: 4, the model you are estimating is:
$$ \Delta y_t = A(B´y_{t−1}+c_0) + B_1\Delta y_{t-1} + B_2\Delta y_{t-2} + B_3\Delta y_{t-3} + B_4\Delta y_{t-4} + \epsilon_t $$
The matrix B is of dimension $n \times r$, and it contains as columns the cointegration vector(s). In your case, $r=1$, and the cointegration vector is
B =
0.7081
1.6282
-2.4581 

The Matrix A represent the "error-correction" matrix. For a system to converge towards the equilibrium cointegration relation (i.e. to be stable), you want these numbers to be in between -2 and 0 (as in your case).
c0 is just a constant of the cointegration relationship (like in a standard function $y=c0+bx$).
The matrices Bi show how previous period shocks translate through the system over time.

> **Comments:**
> **username_0**: Thank you. What about the other paramters? Reading other posts a value greater than +- 2 is significant. Is this the right assumption?  
> **username_1**: @Adrian Can you a bit more specific on which parameters are you refering to? Not sure what you mean.  
> **username_0**: A, B, B1, B2, c0, c1  
> **username_1**: @Adrian what do you think of the update? Still got questions?  

---

