2 p.m.
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). 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.
cheers,
sven
2:51 p.m.
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, $nobs, 1, 3)
0.99383649
this shows that if the test had had the same absolute value but on the
negative side, the probability would be just a little lower, 99.4
percent.
I guess I can see a case for giving a p-value of NA when the test is
on the wrong side of zero, but I wouldn't be comfortable giving it as
1.0. That would be saying the probability of what is 100%?
Allin
3:34 p.m.
Am 05.11.18 um 15:51 schrieb Allin Cottrell:
On Mon, 5 Nov 2018, Sven Schreiber wrote:
>
> open wgmacro.gdt
> adf 0 log(income) --ct # gives pos. test stat
>
> eval urcpval($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 $test under H0, doesn't it?
Well, is a p-value a probability? Suppose in general I run a one-sided
test with H0: b=0 and and H1: b<0. The decision rule is that whenever
the p-value < alpha (which is my own chosen significance level) then
reject H0 in favor of H1. Equivalently reject when the test statistic is
beyond my critical value, and beyond here with an underlying t-stat
would mean "to the left of".
The critical value is <0, and If I get bhat > 0, my t-stat can never be
to the left of the critical value. So one certainly shouldn't reject in
favor of H1. (Maybe in favor of some other hypo, but that is not on the
table here.) So how do I ensure this non-rejection with the p-value
output, i.e. prevent that p < alpha for any alpha \in (0,1)? Either set
p >= 1 or set it to NA.
So no, I don't think it is a probability in general, only in the
standard/easy cases can it be given such an interpretation.
Coming back to this DF case, if for \hat{(rho-1)} > 0 (or rhohat > 1)
one gets already a p-value of <1, what happens if by chance you land
exactly on the H0 value rho = 1? By monotonicity it would also be <1,
but surely if you have an estimate that equals your H0 value you want to
have a p-value of 1!
Well, the answer is given by urcpval(0, 0, 1, 3), which yields
0.99628822. This can't be right!
cheers,
sven
3:53 p.m.
On Mon, 5 Nov 2018, Sven Schreiber wrote:
Am 05.11.18 um 15:51 schrieb Allin Cottrell:
> On Mon, 5 Nov 2018, Sven Schreiber wrote:
>
>>
>> open wgmacro.gdt
>> adf 0 log(income) --ct # gives pos. test stat
>>
>> eval urcpval($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
4:09 p.m.
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
4:52 p.m.
Dear Sven,
eval urcpval($test, $nobs, 1, 3)
eval urcpval(abs($test), $nobs, 1, 3) # same
do
eval $test
Since $test > 0 this is the only expected result
H0: a series has unit root
Most macro indicators have unit roots, the result is expected
t-stats in ADF test under H0 has distribution which
is a functional of the standard Wiener process, so Student's is irrelevant
There are no such thing as two-sided ADF test
The variant you used is by far not the best one
Use GUI to auto-detect lag length
To reproduce GUI version in script the
default max lag length should be entered manually
This example does not indicate any anomalities
Oleh
5 листопада 2018, 18:09:59, від "Sven Schreiber" <svetosch(a)gmx.net>:
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
_______________________________________________
Gretl-devel mailing list
Gretl-devel(a)lists.wfu.edu
http://lists.wfu.edu/mailman/listinfo/gretl-devel
6:11 p.m.
Dear Sven,
To reproduce the best GUI option
with a script, use
open wgmacro.gdt
y = log(income)
maxlag = 12*(nobs(y)/100)^0.25
adf maxlag y --c --ct --test-down
# now no signs of explosion
Oleh
5 листопада 2018, 18:09:59, від "Sven Schreiber" <svetosch(a)gmx.net>:
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
_______________________________________________
Gretl-devel mailing list
Gretl-devel(a)lists.wfu.edu
http://lists.wfu.edu/mailman/listinfo/gretl-devel
6:20 p.m.
Am 05.11.18 um 19:11 schrieb oleg_komashko(a)ukr.net:
Dear Sven,
To reproduce the best GUI option
with a script, use
open wgmacro.gdt
y = log(income)
maxlag = 12*(nobs(y)/100)^0.25
adf maxlag y --c --ct --test-down
# now no signs of explosion
Oleh, that's not the point. It's just an example I came across where the
estimate is on the "wrong" side. It's clear that it doesn't happen very
often with actual data, but it can happen. I would be curious to hear
your opinion about what the correct p-value for a DF test (with as many
lags as you like) is when the test statistic is positive instead of
negative.
cheers,
sven
8:15 p.m.
Dear Sven,
There is no wrong side here
The distribution of ADF statistics is skewed towards left
for tau = -0.12 it is less than for tau = 0.12 as should be
You can test against other soft you will get the same
Explosive behavior is ruled out from the start:
To this end one uses 1): logs
2) integration order 2
There are no ADF tests against explosion
Only a=0 versus a<0
I think, the best way to convince you is
to reproduce the same in another soft
To develop ADFGLS I studied the surface
response methodology
MacKinnon's p-values are very reliable from 5*10^-5 to 1-5*10^5
At far tails they are skewed towards ends, say instead of 10^-7
one can get 10^-15 but this never can difference for inference
Oleh
5 листопада 2018, 20:20:59, від "Sven Schreiber" <svetosch(a)gmx.net>:
Am 05.11.18 um 19:11 schrieb oleg_komashko(a)ukr.net:
Dear Sven,
To reproduce the best GUI option
with a script, use
open wgmacro.gdt
y = log(income)
maxlag = 12*(nobs(y)/100)^0.25
adf maxlag y --c --ct --test-down
# now no signs of explosion
Oleh, that's not the point. It's just an example I came across where the estimate
is on the "wrong" side. It's clear that it doesn't happen very often
with actual data, but it can happen. I would be curious to hear your opinion about what
the correct p-value for a DF test (with as many lags as you like) is when the test
statistic is positive instead of negative.
cheers,
sven
_______________________________________________
Gretl-devel mailing list
Gretl-devel(a)lists.wfu.edu
http://lists.wfu.edu/mailman/listinfo/gretl-devel
7:27 p.m.
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.
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.
Allin
7:43 p.m.
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
9:16 p.m.
New subject: ADF p-value glitch? CHECK against R script
Dear Sven,
to compare run in R
(Rgretl (0.22) and urca (last) shoul be installed
<R>
library(Rgretl)
library(urca)
wgmacro = open_gdt("wgmacro")
l_income = log(wgmacro$income)
tau = ur.df(l_income, type = "trend",lags=0)@teststat
tau3 = tau[1]
pvalue = punitroot(tau3, N = length(l_income), trend = "ct", statistic =
"t")
grscr =
'open wgmacro.gdt -q
adf 0 log(income) --ct -q
matrix test = $test
matrix pval = urcpval($test, $nobs, 1, 3)
'
gradf = run_grcli(grscr,output=list(matr=c("test","pval")))
# checking
abs(tau3 - gradf$test) # tau-stat
abs(pvalue - gradf$pval) #p-values
<R>
Oleh
5 листопада 2018, 21:43:33, від "Sven Schreiber" <svetosch(a)gmx.net>:
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
_______________________________________________
Gretl-devel mailing list
Gretl-devel(a)lists.wfu.edu
http://lists.wfu.edu/mailman/listinfo/gretl-devel
10:34 p.m.
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, $nobs, 1, 3)
</hansl>
The issue is that the AR coeff is slightly explosive (1.003), which is
not in the rejection region of the one-sided DF test. So the test stat
is positive instead of negative, but the p-value given by Gretl is
strictly <1 (0.9971). I know that philosophically a one-sided test is
actually trickier than we tell the students, so I don't mind whether the
"correct" result is 1 or NA, but I'm pretty sure it shouldn't be
<1.
It seems that Gretl just uses the absolute value of the test stat and
thus doesn't differentiate between the left and the right side.
Summary, from my point of view: We're now clear that gretl is not
ignoring the sign of the test statistic, and is doing what R, Stata
and Eviews also do, namely reporting an estimate of the CDF of the
relevant distribution evaluated at the observed test statistic.
Although I think this convention is too strong to be bucked, I do
think that Sven has a point. It's not specific to ADF tests, but
pertains more generally to p-values for one-sided tests. It's not
clear to me that p-values are well defined for values of the test
statistic that are not at all adverse to the null -- unless there's
unique such value, as in a two-sided test, in which case we say it
has a p-value of 1 (the estimate coincides precisely with the claim
made by the null).
Allin
10:53 p.m.
R has another version adf.test {tseries}
which does have "two-sided" alternative
I think somebody can reproduce it in a package
As for me, gretl has excellent correspondence
with most popular textbooks
I use gretl for unit roots even in my R classes
I even do not know where explosive processes
is used even in PhD courses
Oleh
6 листопада 2018, 00:34:59, від "Allin Cottrell" <cottrell(a)wfu.edu>:
On Mon, 5 Nov 2018, Sven Schreiber wrote:
please consider this:
<hansl>
open wgmacro.gdt
adf 0 log(income) --ct # gives pos. test stat
eval urcpval($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
_______________________________________________
Gretl-devel mailing list
Gretl-devel(a)lists.wfu.edu
http://lists.wfu.edu/mailman/listinfo/gretl-devel
7:43 a.m.
On Tue, 6 Nov 2018, Sven Schreiber wrote:
Am 05.11.18 um 23:53 schrieb oleg_komashko(a)ukr.net:
> I even do not know where explosive processes
> is used even in PhD courses
>
I've seen people work with explosive processes to model bubbles.
This, for example:
https://econpapers.repec.org/paper/pramprapa/77254.htm
-------------------------------------------------------
Riccardo (Jack) Lucchetti
Dipartimento di Scienze Economiche e Sociali (DiSES)
Università Politecnica delle Marche
(formerly known as Università di Ancona)
r.lucchetti(a)univpm.it
http://www2.econ.univpm.it/servizi/hpp/lucchetti
-------------------------------------------------------
8:28 a.m.
This, for example
Thank you!
If you decide to include two-sided test
into libgretl,
I think it would be an additional
option, not the replacement.
Oleh
6 листопада 2018, 09:43:46, від "Riccardo (Jack) Lucchetti"
<r.lucchetti(a)univpm.it>:
On Tue, 6 Nov 2018, Sven Schreiber wrote:
Am 05.11.18 um 23:53 schrieb oleg_komashko(a)ukr.net:
> I even do not know where explosive processes
> is used even in PhD courses
>
I've seen people work with explosive processes to model bubbles.
This, for example:
https://econpapers.repec.org/paper/pramprapa/77254.htm
-------------------------------------------------------
Riccardo (Jack) Lucchetti
Dipartimento di Scienze Economiche e Sociali (DiSES)
Università Politecnica delle Marche
(formerly known as Università di Ancona)
r.lucchetti(a)univpm.it
http://www2.econ.univpm.it/servizi/hpp/lucchetti
-------------------------------------------------------
_______________________________________________
Gretl-devel mailing list
Gretl-devel(a)lists.wfu.edu
http://lists.wfu.edu/mailman/listinfo/gretl-devel
3:36 p.m.
Am 06.11.2018 um 09:28 schrieb oleg_komashko(a)ukr.net:
> This, for example
Thank you!
If you decide to include two-sided test
into libgretl,
I think it would be an additional
option, not the replacement.
I agree -- but I'm not sure if anybody actually suggested to add a
two-sided test. I didn't! (Or at least I didn't mean to...)
cheers,
sven
9:11 a.m.
New subject: Bundle within bundle - icon view save ...
It seems that there is a bug when you try to save a bundle that is
already contained in a bundle using icon view.
Although a window opens (with a proposed name for the bundle to be
created) and returns no error when you click OK, the bundle is not
created.
<hansl>
clear
bundle foo
bundle fooinside
M1 = I(3)
scalar c1 = 42
M2 = I(4)
scalar c2 = 43
foo.M1 = M1
foo.c1 = c1
fooinside.M2 = M2
fooinside.c2 = c2
foo.fooinside = fooinside
delete fooinside
delete --type=matrix
delete --type=scalar
</hansl>
At the moment you can do it only through script or the console (for
example add the line: fooinside = foo.fooinside at the end of the
script)
Thanks,
Yiannis
3:01 a.m.
New subject: Bundle within bundle - icon view save ...
On Wed, 7 Nov 2018, Ioannis A. Venetis wrote:
It seems that there is a bug when you try to save a bundle that is
already contained in a bundle using icon view.
Although a window opens (with a proposed name for the bundle to be
created) and returns no error when you click OK, the bundle is not
created.
Thanks for the report, Ioannis. I see what you mean and that is now
fixed in git; snapshots will follow before long.
Allin
11:39 p.m.
Am 05.11.18 um 23:34 schrieb Allin Cottrell:
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 --
Thank you for the summary, Allin, that's exactly what I meant.
(@ all others: thank you for your comments, but it seemed to me that you
were stating or proving things that I had never doubted in the first place)
For those who are still interested in the philosophy of statistics,
after some more reading (browsing, really) I think some of that
differing interpretation of p-values actually dates back to discussions
between Fisher vs. Neyman-Pearson. Fisher apparently advocated the
p-value as a continuous (or monotonous) summary statistic of how well
the data are compatible with the hypothesis. In that sense my doubts
about the one-sided test situation were Fisherian when I said, how can
data that exactly coincides with the H0 value be classified by the
software as *less* compatible (lower p-value, p<1) than data further
away from it.
However, I now actually think there is another layer of complexity added
by the special ADF situation.
In a standard one-sided test setup (non-ADF) the null hypothesis is what
is called "composite", it covers a continuum of values like in H0: b
\geq b_0. So the case bhat > b is no deviation from H0 at all. My old
argument was that P-values in that area are dubious, given that they are
supposed to refer to something "at least as extreme as the observation",
when the observation is not extreme at all.
In the ADF situation instead it really is just the unit-root point
hypothesis. Not composite. So rhohat > 1 is not part of H0, but at the
same time we would never reject H0 because of it. Very strange beast.
P-values in that region also dubious, but perhaps for different reasons.
My conjecture is that many people in R, Stata, Eviews have asked
themselves the same questions, but there is no satisfactory solution to
be communicated in a single number. Fortunately the numerical difference
is small (as someone already mentioned) and so for standard levels of
significance and decision rules it's just not relevant.
The current urcpval results in the upper tail may still be wrong and/or
meaningless when you take the meaning of p-values seriously, but I
concede it's hard to come up with something else which is also concise.
thanks,
sven
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20 comments
5 participants
participants (5)
-
Allin Cottrell -
Ioannis A. Venetis -
oleg_komashko＠ukr.net -
Riccardo (Jack) Lucchetti -
Sven Schreiber