The video shows a table with various trace/eigenvalue tests
what does
r <=0
r<=1
r<=2
mean?
thanks
These are the null hypothesis of the Johansen test.
r<=0
The first one of r<=0 can be interpreted as (null hypothesis) no cointegration relationship between time series. If we are able to reject this null hypothesis then we can conclude that there is at least one cointegrating relationship between the time series.
r<=1
This can be interpreted as (null hypothesis) less than 1 cointegration relationship between time series. If we are able to reject this null hypothesis then we can conclude that there are two cointegrating relationships between the time series.
But what does it mean to have two cointegrating relationships between the time series?
This means that we can form the linear combination of the portfolio in two ways and both will yield a stationary portfolio. When the CADF test was discussed, it was pointed out that is order dependent method. By changing the values of x and y we get different results. But Johansen test is order independent method and it lists out all the ways in which you can combine the time series to form stationary portfolio.
I hope this helps.