Am 01.02.2019 um 09:30 schrieb Sven Schreiber:
urca:
test 10pct 5pct 1pct
r <= 1 | 5.67 6.50 8.18 11.65
r = 0 | 26.35 15.66 17.95 23.52
So that's the differing conclusions from the OP, and Gretl and tsDyn
again agree, urca doesn't.
Some further evidence from Stata's documentation, see
https://www.stata.com/manuals14/tsvecrank.pdf.
There are some critical values for the trace stat printed in the
examples. Note: They have a 3-equation system, whereas in our
(Reynaldo's) example we have 2 equations (2 endogenous). For the
distribution (critical values) what matters is N - r_0 under H0, the
number of I(1) trends under the null. You must not compare their r=0
case with our r=0 directly. This can be confusing here, but I hope I got
it right.
With this in mind, Stata has (Examples 2 and 1):
20.04 where urca has 23.52 (N - r_0 = 2 at 1%)
6.65 where urca has 11.65 (N - r_0 = 1 at 1%)
15.41 where urca has 17.95 (N - r_0 = 2 at 5%)
3.76 where urca has 8.18 (N - r_0 = 1 at 5%)
Notice that with Stata's critical values the test conclusions from
Reynaldo's example would agree with gretl (and tsDyn).
Both Stata and urca claim to use Osterwald-Lenum. Unfortunately I
haven't been able to quickly grab a copy of that paper, so I couldn't
check.
I repeat that I found some MacKinnon et al. paper which at first glance
seemed to support urca.
In any case, gretl is in good company, whereas urca apparently isn't.
cheers,
sven