Re: [Gretl-devel] ADF p-value glitch?
On Mon, 5 Nov 2018, Sven Schreiber wrote:
Am 05.11.18 um 15:51 schrieb Allin Cottrell:
> On Mon, 5 Nov 2018, Sven Schreiber wrote:
>
>>
>> open wgmacro.gdt
>> adf 0 log(income) --ct # gives pos. test stat
>>
>> eval urcpval($test, $nobs, 1, 3)
>> eval urcpval(abs($test), $nobs, 1, 3) # same
OK, this last line was foolish, I was still in my mind in the world of
negative ADF test stats, whereas here the point is exactly that it is
positive.
>
> True, the test statistic is not in the rejection region. Nonetheless, the
> p-value of 0.9971 gives the probability of obtaining an ADF tau value less
> than $test under H0, doesn't it?
Well, is a p-value a probability?
I think it's best described as: the probability, conditional on H0
being true, of obtaining a test statistic as unfavorable to the null
as the one actually observed, or more so.
One could argue that if the test statistic is not even prima facie
unfavorable to the null (on the wrong side of the distribution), the
antecedent is not fulfilled and the p-value is therefore undefined.
But before changing gretl's behavior I'd want to take a look at what
other software does in this sort of case.
Allin