Re: [Gretl-users] Johansen question
On Sun, May 1, 2011 at 5:17 AM, Allin Cottrell
<cottrell(a)wfu.edu> wrote:
>>
>> For a bivariate case, if the trace test rejects c=0 and does not
>> reject c=1, I report c=1.
>
> OK.
>
>> If it is the other way around, then I report c=0 as the test
>> result.
>
> On the trace test, that result would seem anomalous, and
> indicative of a small-sample problem. If there's "enough evidence"
> to reject c=1 (with an alternative of c=2), then concluding that
> c=0 is problematic.
>
Yes, it's an unsatisfactory result in practice, and it actually seems to
happen on a regular basis. Nonetheless, it is known from the very
beginning (cf. Sören Johansen's book for example) that in principle you
need to apply the tests in a sequence from 0 to n-1, and never mind the
test results that come later in the sequence, if you already accepted an
earlier hypothesis. Otherwise you don't get a test setup with a
controlled overall size. (Apart from that, I also believe that it's not
necessarily a small-sample phenomenon, but so far that's just a hunch.)
cheers,
sven