Interpretation of Johansen cointegration test with three variables, number of cointegrating vectors, number of common tr

For econometric discussions not necessarily related to EViews.

Moderators: EViews Gareth, EViews Moderator

eviews1
Posts: 18
Joined: Mon May 02, 2016 8:55 am

Interpretation of Johansen cointegration test with three variables, number of cointegrating vectors, number of common tr

Postby eviews1 » Mon Apr 17, 2017 8:49 am

Hello,

I run a few Johansen cointegration test on made series (data were generated in MATLAB) . I am trying to interpret the meaning of a number of cointegrating vectors and a number of common trends. These are my tests.

We have three series x(t), y(t) and z(t)

1) Scenario 1 (make y follow x and z wander by itself):

x(t)=x(t-1)+v(t), x(t) is RW, it wanders by itself
y(t)-y(t-1=-alpha*(y(t-1)-x(t-1))+m(t); y(t) follows x(t); the 1st coint relation is in the bracket
z(t) = z(t-1)+u(t) z(t) is RW, it wanders by itself

x wanders by itself, y follows x and z wanders by itself. Theoretically, the Johansen test should reject no cointegration and then should not reject
at most one cointegration, i.e. there is one cointegrating vector and (3-1)=2 common trends.

The test was run with the following settings:
Intercept(no trend) in CE - no intercept in VAR (2nd option), and lag intervals: 0 0

Q1) Were there any test setting misspecifications?

From the test I get: "Near Singular Matrix".
Q2) Does the test refer to PI matrix (see below)?
Q3) Why don't I get rejection of no cointegration and then subsequently no rejection of "at most one cointegrating vector"?
Q4) How to construct two series so that I get rejection of no cointegration and no rejection of “at most one”? I thought y follows x and z wnaders by itself should be that case.
So if we have in a matrix form beta*X(t) = EPSILON(t) where EPSILON is stationary by definition of cointegration and beta
beta is a matrix of cointegrating parameters.
Then in the ECM form we have deltaX(t)=alpha*EPSILON(t-1)+U(t) => deltaX(t)=alpha*beta*X(t-1)+U(t)=PI*X(t-1)+U(t)

2) Scenario 2 (make y and z follow x):

x(t)=x(t-1)+v(t), x(t) is RW, it wanders by itself
y(t)-y(t-1=-alpha*(y(t-1)-x(t-1))+m(t); y(t) follows x(t); the 1st coint relation is in the bracket
z(t) = x(t)+u(t) z(t) is cointegrated with x(t); the 2nd coint relation in the system

x wanders by itself, y and z follow x. Theoretically, the Johansen test should reject no cointegration, reject "at most one" coint vectors and should
not reject "at most two" cointegrating vectors, i.e. there are two cointegrating vectors and (3-2)=1 common trend. It means x goes by itself (it leads) and two other follow x.

From the test I get what is theoretically expected (I tried with 200 obs and 54 obs) => there is 1 common trend.

Q5) I interpret 1 common trend as series x leads two other series (by construction I did that), am I right?

Q6) What could be no sufficient sample size for the cointegration test?

Thank you.

Argyn

Return to “Econometric Discussions”

Who is online

Users browsing this forum: No registered users and 18 guests