Am 05.11.18 um 16:53 schrieb Allin Cottrell:
> On Mon, 5 Nov 2018, Sven Schreiber wrote:
>
>>>
>> 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.

I'm not against it. (As I said from the beginning, p-values can be 
philosophically tricky, and one-sided tests, too.)

However, this still leaves the wrong result of urcpval(0,0,1...). I 
think your definition also says it should be 1. Or to put it 
differently: The current output can only be justified with your 
definition if at the same time you consider explosive values (possibly 
far away from 1) as _less_ unfavorable to the unit root H0 than the H0 
value of 1 itself. I don't think we'd want that.

>
> 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.

Right. I think that's an important difference with one-sided tests, 
where we cannot just focus on the null and forget about the rest.

I mean, one _could_ do the whole thing as a two-sided test, also 
allowing explosion under the null. Obviously the null distribution would 
be asymmetric. But that would also affect the critical values to the 
left (stationary) side, because a part of the prob mass of the rejection 
region would have to be shifted to the right.

(I'm not sure in the end / right now what gretl is actually doing 
effectively.)


> 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.

thanks,

sven

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