Johansen Cointegration Result Interpretation

[hanafi_sudirman]

Morning All,

I'm unfamiliar in the field of econometrics, but need the cointegration test for my thesis. So i was hoping on your help in telling me whether i'm on the right track and how to interpret my results. currently i am using eviews version 7.1

So my thesis is about cointegration between 6 indices in ASIA and i have 6 time series (2189 daily data), I have tested them all using ADF and they were all non stationary in level and stationary in first difference.

Down here i have the results, but how do i interpret them, i mean what are these results telling me? And what is the different conclusions in Trace and Max Eigenvalue? What is my next step i mean what test should i take further? Does it means that all variable are cointegrated (it says that "Trace test indicates 6 cointegrating eqn(s) at the 0.05 level")?

If i would like to estimate the max portofolio of these 6 indices, what tools should i use?

Thank you very much

Regards,
Hanafi

[hana88]

Hello All,

I'm also having the same problem. Not sure how to interpret this

Appreciate if anyone can help.

Thanks.

[nishantvats12]

Hi Hanafi,

As for your first point, the fact that all variables are integrated of same order should be an enough inspiration (from econometrics perspective) for you to justify Johanson Jesulius (JJ) test. But it is customary in research to validate this via other tests of unit root like KPSS, DF-GLS and PP test. Also, many researchers hold the view that Zivot-Andrews test should be applied to check if the null hypothesis was being rejected due to the presence of a structural break in the data. Hence, you can also try the same. Zivot Andrews (ZA) test is available in Eviews 8.0 and also as a plug-in in its lower version. Refer to the Eviews website for more details on ZA test.

Given that after you have established that all variables are integrated of the same order, JJ test should be your next step. From what I observe from your result sets, you have rejected the null hypothesis of no co-integration and established presence of 5 co-integrating equations based on both the Trace and Maximum Eigen value statistic. I assume you have selected the lag length for the test based on either minimum SIC or AIC value.

The next step would be to estimate a VECM with 5 co-integrating equations. So go ahead and explore the world of econometrics with your thesis. Hana, I hope you would also get your answer via this
reply. Eviews help guide is really good to start understanding applied econometrics. In addition you can also find some video lectures on how to apply VECM and JJ test and their interpretation on youtube. I would also recommend you to understand the evolution and the methodology of both of these to gain a better understanding.

Best of Luck!!!

Nishant Vats

[hana88]

Hi Nishant,

Thank you very much for your response! Yup I've been exploring the videos on youtube, some are pretty straightforward and easy to understand (Godbless these people). However I've noticed that most of the examples resulted in the same conclusion for max eigenvalue and trace tests. What if what I obtained is different for each? (you may refer to the file as attached in my previous message).

Thanks again Nishant. Anyone who has any idea how to interpret this feel free to voice it out :)

[nishantvats12]

Hi Hana,

I can't recall the reference for what I am going to tell you so you are free to explore other alternatives.
Usually, in practice if the system is bi-variate (consisting of two variables) trace statistic is generally used. However, in case of a multivariate frame (with variables more than 2) it has been seen that Max Eigen value has greater power. Hence, in a multivariate structure it is better to follow Max Eigen value statistic.

You can follow the blog by Prof. Giles (Econometrics Beat), he has given some very nice insights into VECM framework and Granger causality.

Hope this helps.

Regards
Nishant Vats

[nishantvats12]

Hi Hana,

I was reading another articles today which says in case of a contradiction between trace and eigen value statistics, go with the trace statistic, however, no specific reason has been given for the same.
The article is attached here.

I am again unsure if literature in error correction model has a consensus on this idea. I wish if trubador reads this post and could clarify on this.

[trubador]

Using VECM models on daily data can be problematic. You may have to deal with the noise at the outset or prefer to work in lower frequencies.

As for "Interpreting Results of a Johansen Cointegration Test", please read the page 853 of Users Guide II. The following warnings are from there:

• Critical values are available for up to k 10 series. Also note that the critical values depend on the trend assumptions and may not be appropriate for models that contain other deterministic regressors. For example, a shift dummy variable in the test VAR implies a broken linear trend in the level series yt.

• The trace statistic and the maximum eigenvalue statistic may yield conflicting results. For such cases, we recommend that you examine the estimated cointegrating vector and base your choice on the interpretability of the cointegrating relations; see Johan- sen and Juselius (1990) for an example.

• In some cases, the individual unit root tests will show that some of the series are integrated, but the cointegration test will indicate that the P matrix has full rank (r=k). This apparent contradiction may be the result of low power of the cointegration tests, stemming perhaps from a small sample size or serving as an indication of specification error.

Lütkepohl et al. (2000) compare these tests and conclude that "[...] trace tests are advantageous if there are at least two or more cointegrating relations in the process than specified under the null hypothesis." You can read the full study at: http://edoc.hu-berlin.de/series/sfb-373 ... PDF/83.pdf

[nishantvats12]

Hi Trubador,

Can you elucidate something on the interpretation of the unrestricted cointegrating and adjustment coefficients. I have attached a workfile.
I understand the interpretation of this in mathematical sense to find out the rank, but I want to know the physical interpretation of it. I would be glad if you could help me.

Regards
Nishant Vats

[nishantvats12]

Any help with regard to my previous question?

[heba90]

Hello everyone can you help me interpret these results i am a bit confused whether there is a cointegration or not I am doing work for my thesis and i want to do a VEC model do i have cointegration or not?
Date: 04/18/15 Time: 17:42
Sample (adjusted): 2005Q2 2013Q4
Included observations: 35 after adjustments
Trend assumption: Linear deterministic trend
Series: CR MR_BETA EFFICIENCY_RATIO ROA LOAN_GROWTH_RATE
Lags interval (in first differences): 1 to 4

Unrestricted Cointegration Rank Test (Trace)

Hypothesized Trace 0.05
No. of CE(s) Eigenvalue Statistic Critical Value Prob.**

None * 0.839862 128.2216 69.81889 0.0000
At most 1 * 0.514890 64.11154 47.85613 0.0007
At most 2 * 0.432954 38.79323 29.79707 0.0035
At most 3 * 0.285672 18.93724 15.49471 0.0145
At most 4 * 0.185068 7.162777 3.841466 0.0074

[heba90]

I am sorry the one confusing me is

Date: 04/18/15 Time: 15:06
Sample (adjusted): 2004Q3 2013Q4
Included observations: 38 after adjustments
Trend assumption: Linear deterministic trend
Series: CR MR ROA TA EFFICIENCY
Lags interval (in first differences): 1 to 1

Unrestricted Cointegration Rank Test (Trace)

Hypothesized Trace 0.05
No. of CE(s) Eigenvalue Statistic Critical Value Prob.**

None 0.408462 50.61688 69.81889 0.6108
At most 1 0.273698 30.66577 47.85613 0.6844
At most 2 0.219450 18.51375 29.79707 0.5283
At most 3 0.135667 9.099004 15.49471 0.3563
At most 4 0.089399 3.558715 3.841466 0.0592

[heba90]

both results are weird

[muslimah]

* sign indicated that your null hypothesis ( no cointegration ) is rejected. It Means your variables have cointegration. test shows that there are 5 cointegrating equations.

[muslimah]

Nishant thank you soo much for clearing my concepts.

[stuart92s]

hello all,

i currently doing my research and well to tell the truth, im quite newbie when came to economics, but its better to learn than nothing rite? anyway, i still get confuse whether do all the variables need to be in a loglin mode? because when i use this method for johansen cointegration test, i get these result :

Date: 05/09/15 Time: 23:30
Sample (adjusted): 1984 2013
Included observations: 30 after adjustments
Trend assumption: Linear deterministic trend
Series: LNLFPR LNGDP LNPOP LNEDU LNETH LNGA
Lags interval (in first differences): 1 to 1

Unrestricted Cointegration Rank Test (Trace)

Hypothesized Trace 0.05
No. of CE(s) Eigenvalue Statistic Critical Value Prob.**

None 0.623143 84.34146 95.75366 0.2347
At most 1 0.569076 55.06475 69.81889 0.4163
At most 2 0.434539 29.81007 47.85613 0.7286
At most 3 0.292136 12.70663 29.79707 0.9045
At most 4 0.071760 2.341544 15.49471 0.9889
At most 5 0.003580 0.107582 3.841466 0.7429

Trace test indicates no cointegration at the 0.05 level
* denotes rejection of the hypothesis at the 0.05 level
**MacKinnon-Haug-Michelis (1999) p-values

the results shows tht there is no cointegration at all... did i made a mistake here? need help A.S.A.P.. tq