I suspect that your series may be too short to support this analysis. I presume you have some underlying economic model and the interpretation should be made in terms of your underlying model. The Johansen methodology is not a search procedure to find a good model to fit s data set.

Your cointegration relationship is estimating long-run elasticities. You must judge these in terms of your model. One generally does not attach importance to individual coefficients in the short run. It is possible that you could do Granger causality tests or Impulse response functions.

Have you completed any specification tests - heteroskedasticity, autocorrelation, stability tests, etc? You can not make any inferences if your data and theory are not congruent.

You might also have a look at the econometrics package which is free and can be downloaded from https://gretl.sourceforge.net/. This covers the analysis that you are doing and is much easier to learn than R.

Dear professor John,

Many thanks for your response. Before VECM model, I did Johansen cointegration and tested there is 1 cointegration equation in Trace test. ADF test performed for stationarity.Then performed VAR model to test stability for this ran correlogram all the residuals are within the lines and LM test p-values are more than 5% for all the 8 lags so there is no autocorrelation.Also ran impulse response function. I am doing my thesis for my masters. The topic is cointegration of cryptocurrency using Johnson cointegration and VAR/VECM models for 4 cryptocurrency.

Please advise me if anything that needs to be undertaken and how to interpret these results for my master thesis.

I presumethat you are using EVIEWS. I have not used EVIEWS for many years and do not have acces to it or to an EVIEWS manual.

I read your cointegrating equation as

ecm = log BTC -0.67 log ETh + 0.30 logxlm -0.68 log XMR -1.50

If this is correct in the long run a 1% rise in ETH causes a .67% fall in BTC, etc. (Check your EVIEWS manual to see that the signs of the coefficients should be reversed). This equation hold at each equilibrium. At equilibrium a shock to one variable will cause the system to move to another equilibrium. This equation holds in both equilria. Impulse response functions track the transitions.

There are two problems with the interpretation of the equilibrium relationship.

Judging significance in these circumstances is much more difficult. I would recommend that you consult a text book such as Enders (2014), Applied Econometric Time Series, 4th edition,Wiley and your software manual to check how to make inferences on these coefficients.

When you test the significance of a coefficient, depending on the value of your test statistic, you can come to one of two conclusions

1 the coefficient is significantly different fro zero

2 The coefficient is not significantly different from zero. This does not mean that the statistic is zero. Again you should be making conclusions on your theoretical model and the questions that arise from the model. One of the most common cause of getting a lot of insignificant coefficients is having insufficient data to answer your questions.

You have choosen a difficult piee of econometrics for your thesis. There is a lot of econometrics/statistics in a VECM analysis that is not covered in elementary textbooks. I am not familiar with your knowledge of mathematics, statistics or computing and I am reluctant to go into more detail. I would advise you to talk to your supervisor to determine exactly what you are expected to do.

Hey Kiran,

VAR and VECM models are usually tested together and the model chosen is based on stationarity and cointegration. Hence, there is a sequence of steps to be taken for this type of modelling. See the following link: https://www.projectguru.in/regression-analysis-using-var-stata/

Steps and interpretation can be found above and in the entire series of articles.

Your model may be underspecified as well. You should run the lag selection tests to see if greater lags should be included.

Suppose you have estimated a VECM model to study the relationship between GDP growth and inflation in a country. The model includes two error correction terms (ECTs), one for GDP growth and one for inflation. The estimated coefficients for the error correction terms are as follows:

• GDP growth ECT: -0.5 (p-value = 0.01)
• Inflation ECT: 0.3 (p-value = 0.10)

In this case, the GDP growth ECT is negative and statistically significant, while the inflation ECT is positive but not statistically significant. This suggests the following:

• In the short run, a positive deviation from the long-run equilibrium relationship between GDP growth and inflation will be corrected in the case of GDP growth, but will be exacerbated in the case of inflation.
• In the long run, a positive deviation from the long-run equilibrium relationship between GDP growth and inflation will be corrected in the case of GDP growth, but will persist in the case of inflation.

This interpretation is based on the magnitude and statistical significance of the error correction terms. However, it is important to keep in mind that these are just estimates, and it is always a good idea to consider the robustness of the results to different specifications of the model.

Jamal Tikouk

I totally agree