[Gretl-users] johansen

[Allin Cottrell]

On Thu, 21 Dec 2006, I wrote:

> First, the results you reported earlier:
>
> Rank Eigenvalue   trace  p-value   l-max   p-value
>
>   0    0.11637  13.736  0.3151    11.01    0.2600
>   1    0.030163  2.726  0.6392     2.73    0.6380
>
> Second, the guide from the gretl manual, adapted to the case of
> just 2 variables:
>
> Rank	  Trace test	     Lmax test
> 	   H0	  H1	      H0     H1
>  ---------------------------------------
>   0	  c = 0  c = 2       c = 0  c = 1
>   1	  c = 1  c = 2       c = 1  c = 2
>
> So, using alpha = 0.05 (or alpha = 0.10 for that matter):
>
> Trace test:
>   H0: c = 0: p-value 0.3151, fail to reject (so stop here)

I'll add one more point here (sorry if I'm trying the patience of 
some; I know this not in any way gretl-specific).

These are asymptotic tests, and in large samples you'd expect to 
the see the p-values increasing monotonically as you read down the 
"Trace test" column in the results.  (Loosely, you should have a 
better chance of rejecting c = 0 using an alternative of c = 1 
than using an alternative of c = 2, and so on.)

However, in some small samples this can be inverted.  If I 
remember right, I've seen cases where it would seem that you'd 
reject c = 0 against an alternative of c = 2, at some standard 
significance level, but not against c = 1.  If you see that sort 
of thing, it really means that you need more data.

Allin.