Am 24.08.2020 um 02:34 schrieb Mike @me.com:
Hi All,
I am trying to determine if two time series (closing prices of two
securities)are cointegrated. The two pass the eyeball test.
I have conducted both the Johansen and Engle-Granger tests. The results
are attached.
I don’t know how to interpret the results. I was hoping for a big “YES”,
“NO” or at least a “LIKELY” at the end of the tests.
Well, statistical tools such as gretl cannot draw the conclusions for
you. One (among many other) reason is that different people prefer
different significance levels.
If anyone would tell me which statistics I should be looking at and how
to interpret them, I would sure appreciate it.
However, in your case it seems pretty clear. (BTW it seems you chose the
"verbose" option, right? There are a lot of auxiliary results in the
output.)
If you look at the top of your page 2 for the Johansen output you find
the so-called Rank tests. You want to test the null of rank=0, so the
first row. The pvalue is below 0.001, so very clear rejection of H0,
thus strong evidence against absence of cointegration, probably as
expected in this case. (Non-statisticians would say evidence in favor of
CI.)
BTW, I would ignore the output "Corrected for sample size". The ad-hoc
method behind these numbers is outdated, maybe we should retire that. In
this case you do not have a small sample anyway. (But if you did, you
would have to use the contributed package "johansensmall" by yours truly.)
hth,
sven
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