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