Am 05.11.18 um 20:27 schrieb Allin Cottrell:
> On Mon, 5 Nov 2018, Sven Schreiber wrote:
>
>> Am 05.11.18 um 16:53 schrieb Allin Cottrell:
>>
>>> But before changing gretl's behavior I'd want to take a look at what 
>>> other software does in this sort of case.
>>>
>> That is certainly wise.
>
> "Everyone" (well, so far R and Stata) gives just what we do, namely 
> the cdf of the tau (or other relevant) distribution evaluated at the 
> observed statistic. So for tau > 0 the quoted p-values are close to 
> but less than 1.0.
>
> My specific comparisons were with adf.test and pp.test in R (tseries) 
> and "dfuller" in Stata.


Thanks for checking, this is interesting of course. I will look around a 
little bit for example in Stata user forums if there has been a 
discussion about this issue. So far I still think it's wrong.

>
> I don't think we want to go out on a limb on this point. Also, I think 
> it's possible to give a coherent interpretation of those p-values 
> close to but short of 1: namely, it's not _impossible_ that you could 
> get a positive tau in a finite sample even if the series in question 
> were stationary -- just very unlikely.
>
>
I still don't think p-values are meant for this interpretation. I guess 
the most glaring incarnation of my problem with this is the case where 
your estimate happens to be right at H0: bhat = b_0. (A probability-zero 
event I know, but a useful thought experiment nonetheless.) How can you 
_not_ have a p-value =1 in this case?? Otherwise it's possible in 
principle to reject the null when the point estimate is identical to the 
null value. This makes no sense to me.

thanks,

sven

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