The Johansen test determines the number of cointegration relationships by examining the rank of the cointegration matrix. It uses trace and maximum eigenvalue statistics to test the null hypothesis of r cointegration vectors against the alternative of r+1 or more. The number of cointegration relationships is identified by finding the largest r for which the null hypothesis cannot be rejected.
The Johansen test determines the number of cointegration relationships between multiple time series variables.
1. Cointegration - Overview, History, Methods of Testing - Corporate Finance Institute
My understanding is that you have three variables
1. price of Bitcoin,
2. price index of a portfolio of IT stocks
3. price of Ethereum
You should be analyzing the logarithms of these variables. If you are not you should restart your analysis.
3 cointegrating vectors imply that all three variables are stationary - a contradiction to the tests that you reported in an earlier question.
2 cointegrating vectors imply that all three pairs of the variables are cointegrated. This implies that the two crypto prices are cointegrated. I have looked at these and as far as I can see they are not cointegrated. This again is a contradiction.
Have you considered the meaning of a quadratic time trend in your data? Eventually, the quadratic time trend will take over and all other effects will be irrelevant.
I have extracted your crypto price data from Yahoo. If you post your portfolio data here I will look at it. I suspect my conclusion will be that there is no long-term equilibrium between the three series. Econometrics can not estimate a relationship that does not exist. Searching may lead to something spurious.
If you do find a stable long-term relationship you will make a fortune.
The trace test is regarded as superior to the max-eigenvalue test. The choice between the two would be made by considering the underlying economic theory and the detailed test table. I do not see how you can justify two cointegrating vectors.
Johansen test of cointegration is all about the determination of the existence of long run relationship amongst variables captured in an econometric model. The condition is that if there exist alleast one cointegration at both trace and max. eigen test. However if there exist atleast one cointegrating equation at at any of the test, we can accept the existence of a long run relationship
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