Am 31.01.2019 um 16:07 schrieb Reynaldo Senra: Ah OK, I see. Right now I don't know a full answer to the question, but it certainly should be clarified. From the ca.jo documentation (in R / urca package I think)  it appears that he uses the Osterwald-Lenum 1992 critical values. Gretl, in contrast, uses a later paper by Doornik (1998) (check the help for coint2). Also it seems that somebody else had a very similar question comparing ca.jo and Python's statsmodels: https://github.com/statsmodels/statsmodels/issues/5355 That thread also seems to end without a real answer. Is Osterwald-Lenum obsolete? thanks, sven

Am 31.01.2019 um 16:07 schrieb Reynaldo Senra: See also https://www.rdocumentation.org/packages/tsDyn/versions/0.9-44/topics/rank... which also uses Doornik's values. Could you compare those two different tools in R? (There's no unique R way there.) cheers, sven

On Fri, 1 Feb 2019, Sven Schreiber wrote: Here's a replication and extension of Sven's exercise. It's not trivial to get R's tsDyn and urca packages to perform the same test but I think I've succeeded. Note that using include="const" in tsDyn is equivalent to ecdet="none" in urca. <hansl> open denmark coint2 4 LRM LRY --quiet foreign language=R --send-data require(tsDyn) cidat <- gretldata[,1:2] # again LRM LRY ve <- VECM(cidat, lag=3, estim="ML", include="const") ve_test0 <- rank.test(ve, r_null=0, type="trace") ve_test0 ve_test1 <- rank.test(ve, r_null=1, type="trace") ve_test1 require(urca) test2 <- ca.jo(cidat, type="trace", K=4, ecdet=c("none")) summary(test2) end foreign </hansl> The relevant portions of the output: --------------------------- gretl (omitting the presumably more reliable small-sample p-values that gretl provides): Rank Eigenvalue Trace test p-value Lmax test p-value 0 0.19415 11.904 [0.1633] 11.009 [0.1557] 1 0.017402 0.89533 [0.3440] 0.89533 [0.3440] R, tsDyn: Test of rank 0 versus 2 (trace test), p-value: 0.1633226. Test of rank 1 versus 2 (trace test), p-value: 0.344037. R, urca: Test type: trace statistic , with linear trend Values of teststatistic and critical values of test: test 10pct 5pct 1pct r <= 1 | 0.9 6.50 8.18 11.65 r = 0 | 11.9 15.66 17.95 23.52 --------------------------- Gretl and tsDyn are clearly agreed. What about urca? Note that the two tests appear in the opposite order relative to gretl and tsDyn. a) Since "test" = 0.9 is less than "10pct" = 6.50, H0 is not rejected at the 10% level. Agreed, since gretl and tsDyn show p-value = 0.344. b) Since "test" = 11.9 is less than "10pct" = 15.66, H0 is not rejected at the 10% level. Agreed, since gretl and tsDyn show p-value = 0.1633. So I think we await a fully-specified example of disagreement between R::urca and R::tsDyn or gretl. Allin

Am 01.02.2019 um 06:49 schrieb Artur T.: Artur, please wait until this issue is settled and we know what's going on. (BTW, are you in Australia or something that you're up at 6:49 UTC+1, hehe?) cheers, sven

On Thu, 31 Jan 2019, Allin Cottrell wrote: Just let me add that, if you want state-of-the-art p-values, you should use Sven's "johansensmall" package. There is quite a lot of evidence that small sample issues can be substantial in cointegration testing. But that's beside the point, I guess. ------------------------------------------------------- Riccardo (Jack) Lucchetti Dipartimento di Scienze Economiche e Sociali (DiSES) Università Politecnica delle Marche (formerly known as Università di Ancona) r.lucchetti(a)univpm.it http://www2.econ.univpm.it/servizi/hpp/lucchetti -------------------------------------------------------

Am 01.02.2019 um 07:49 schrieb Riccardo (Jack) Lucchetti: A bit off-topic yes, but OTOH gretl's own ad-hoc "small-sample" predate the johansensmall package (which is also Andreas's BTW), and maybe something should be done about how they're presented. To be clear, they certainly don't do any harm compared to the asymptotical critical values. You're right that users should know that even those built-in "corrected" p-values are still much too low in typical samples (test is oversized). cheers, sven

Am 01.02.2019 um 09:30 schrieb Sven Schreiber: 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

Am 01.02.2019 um 15:04 schrieb Reynaldo Senra: In terms of modeling, you can do whatever you want (well, almost). Just don't expect the rank test to be still correct, then. If this refers to Johansen / Mosconi / Nielsen then this is correct (if no other mistakes are made). But this is not identical to the standard Johansen rank test, especially with respect to the distributions/critical values. In any case, thanks for the report. I'm still curious to learn what's actually the matter with urca's critical values. cheers, sven

Am 01.02.2019 um 17:51 schrieb Allin Cottrell: Thanks, interesting. However, I don't think that it is necessarily wrong per se. This is exactly the problem why the people from Copenhagen and Oxford tried to promote only the usage of the cases where the tests are (asymptotically) "similar" (terminus technicus here). And the unrestricted constant case is not, it depends on whether a trend is actually in the data or not. (I hope I'm not misrepresenting their opinions.) So one could interpret the urca choice as trying to be on the safe side, at the cost of having a conservative test (asymptotically). Another question is whether that was done consciously. So that would settle the issue. Maybe I'm going to tell the statsmodels people (linked earlier in this thread) about those insights. cheers, sven

Am 01.02.2019 um 20:47 schrieb Allin Cottrell: Well, but the statistical model is more general in this case. That's not what we typically call mis-specified. I'd say it's more subtle. But I agree there's a reason why this setup didn't become standard. -s

Am 01.02.2019 um 22:58 schrieb Allin Cottrell: Yes, but the underlying fact that tended to be forgotten is that using the unrestricted constant case only works conditional on a drift term in the data that is actually there. The attached example simulates the case of a trivial non-cointegrated (but integrated) system without any drift (== no linear trend in the data). The resulting 95% quantile matches urca's critical value (N-r_0 = 2 at 5%). Using R's tsDyn, or gretl, or Stata with the unrestricted constant choice on this example would yield biased tests (reject too often, because there the critical value is around 15 instead of 18). This is not the fault of these programs, because the user test spec is "wrong", but in that sense R's urca is on the safe side. But don't get me wrong: I think urca's communication is confusing and the fact that you don't get the standard 5 cases there is not good. cheers, sven

Am 05.02.2019 um 12:51 schrieb Paolo Chirico: Hi, not sure if I understand, because the following works as expected: <hansl> nulldata 10 series x = normal() bundle b = null series b.s = x smpl 1 5 series check = b.s eval nobs(check) eval nobs(b.s) </hansl> cheers, sven