On Mon, 5 Nov 2018, Sven Schreiber wrote:

> please consider this:
>
> <hansl>
> open wgmacro.gdt
> adf 0 log(income) --ct # gives pos. test stat
>
> eval urcpval($test, $nobs, 1, 3)
> </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). I know that philosophically a one-sided test is 
> actually trickier than we tell the students, so I don't mind whether the 
> "correct" result is 1 or NA, but I'm pretty sure it shouldn't be <1.
>
> It seems that Gretl just uses the absolute value of the test stat and 
> thus doesn't differentiate between the left and the right side.

Summary, from my point of view: We're now clear that gretl is not 
ignoring the sign of the test statistic, and is doing what R, Stata 
and Eviews also do, namely reporting an estimate of the CDF of the 
relevant distribution evaluated at the observed test statistic.

Although I think this convention is too strong to be bucked, I do 
think that Sven has a point. It's not specific to ADF tests, but 
pertains more generally to p-values for one-sided tests. It's not 
clear to me that p-values are well defined for values of the test 
statistic that are not at all adverse to the null -- unless there's 
unique such value, as in a two-sided test, in which case we say it 
has a p-value of 1 (the estimate coincides precisely with the claim 
made by the null).

Allin
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