Re: [Gretl-devel] ADF p-value glitch?
On Mon, 5 Nov 2018, Sven Schreiber wrote:
Hi,
please consider this:
<hansl>
open wgmacro.gdt
adf 0 log(income) --ct # gives pos. test stat
eval urcpval($test, $nobs, 1, 3)
eval urcpval(abs($test), $nobs, 1, 3) # same
# just memo, irrelevant:
eval urcpval($test, 0, 1, 3) # asy
</hansl>
The issue is that the AR coeff is slightly explosive (1.003), which is
not in the rejection region of the one-sided DF test. So the test stat
is positive instead of negative, but the p-value given by Gretl is
strictly <1 (0.9971).
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 $test under H0, doesn't it?
If you do
? eval urcpval(-$test, $nobs, 1, 3)
0.99383649
this shows that if the test had had the same absolute value but on the
negative side, the probability would be just a little lower, 99.4
percent.
I guess I can see a case for giving a p-value of NA when the test is
on the wrong side of zero, but I wouldn't be comfortable giving it as
1.0. That would be saying the probability of what is 100%?
Allin