Re: None-uniform distribution of the p-value from ADF test in gretl when there is an intercept or trend? (Sven Schreiber)
1:14 a.m.
Am 25.04.2019 um 06:17 schrieb Fred Engst:
>>
>> I guess you didn't do anything wrong. When the null hypothesis is
>> true and a test is working as designed, its p-value will be
>> uniformly distributed on (0,1). Then using marginal significance
>> level alpha you'll reject 100*alpha percent of the time, and the
>> test is properly sized. Funny how probability works.
>>
>> Allin
>
> Thanks Allin.
> That is interesting indeed. In other words, with an uniform distribution of the
p-value [when y(t) = y(-1)], there is only 5% changes that we do reject the null of random
walk at 5% level of significance.
> However, for other parameters of the intercept or trend, the p-value distribution is
not uniform. So their size is incorrect?
> For example, when I set both the intercept and trend parameters to 0.1, I get the
attached table.
Hi Fred, your DGP is wrong.
When you apply your formula:
y = b0 + rho*y(-1) + b1*index + e
For non-zero b1 and rho=1 the trend term will be cumulated and will
result in a quadratic trend. This is a case not covered by the standard
ADF tests.
cheers
sven
Thanks Sven,
But I’m more confused.
If you are right, then what does the option "--ct (with constant and trend)” as
stated in gretl's documentation mean for ADF test?
If I set both the intercept and trend parameters to 0.1, doesn’t the option “--ct” in DGP
become
y(t)=0.1 + 0.1*t + y(t-1)+ e ?
Fred
7:02 a.m.
New subject: None-uniform distribution of the p-value from ADF test in gretl when there is an intercept or trend? (Sven Schreiber)
Am 26.04.2019 um 03:14 schrieb Fred Engst:
> Hi Fred, your DGP is wrong.
>
> When you apply your formula:
> y = b0 + rho*y(-1) + b1*index + e
>
> For non-zero b1 and rho=1 the trend term will be cumulated and will
> result in a quadratic trend. This is a case not covered by the standard
> ADF tests.
>
> cheers
> sven
>
Thanks Sven,
But I’m more confused.
If you are right, then what does the option "--ct (with constant and trend)” as
stated in gretl's documentation mean for ADF test?
If I set both the intercept and trend parameters to 0.1, doesn’t the option “--ct” in DGP
become
y(t)=0.1 + 0.1*t + y(t-1)+ e ?
In the unit root case the DGP and the test equation are not the same as
regards the included terms. That's because of the implicit cumulation of
exogenous terms in the DGP. The ADF test options refer to the test
equation, not to the DGP equation (under H0).
This is a general property and not specific to gretl.
hth,
sven
5:34 p.m.
New subject: None-uniform distribution of the p-value from ADF test in gretl when there is an intercept or trend? (Sven Schreiber)
On Fri, 26 Apr 2019, Sven Schreiber wrote:
>> cheers
>> sven
>>
>
> Thanks Sven,
> But I’m more confused.
> If you are right, then what does the option "--ct (with constant and
> trend)” as stated in gretl's documentation mean for ADF test?
> If I set both the intercept and trend parameters to 0.1, doesn’t the option
> “--ct” in DGP become
> y(t)=0.1 + 0.1*t + y(t-1)+ e ?
In the unit root case the DGP and the test equation are not the same as
regards the included terms. That's because of the implicit cumulation of
exogenous terms in the DGP. The ADF test options refer to the test
equation, not to the DGP equation (under H0).
This is a general property and not specific to gretl.
And the practical implication is that for Fred's DGP,
y(t)=0.1 + 0.1*t + y(t-1)+ e
where the 0.1*t cumulates, the adf-test option that should yield a
uniformly distributed p-value is --ctt (constant and quadratic trend).
Allin
5:54 p.m.
New subject: None-uniform distribution of the p-value from ADF test in gretl when there is an intercept or trend? (Sven Schreiber)
Am 26.04.2019 um 19:34 schrieb Allin Cottrell:
On Fri, 26 Apr 2019, Sven Schreiber wrote:
>>> cheers
>>> sven
>>>
>>
>> Thanks Sven,
>> But I’m more confused.
>> If you are right, then what does the option "--ct (with constant and
>> trend)” as stated in gretl's documentation mean for ADF test?
>> If I set both the intercept and trend parameters to 0.1, doesn’t the
>> option “--ct” in DGP become
>> y(t)=0.1 + 0.1*t + y(t-1)+ e ?
>
> In the unit root case the DGP and the test equation are not the same as
> regards the included terms. That's because of the implicit cumulation of
> exogenous terms in the DGP. The ADF test options refer to the test
> equation, not to the DGP equation (under H0).
>
> This is a general property and not specific to gretl.
And the practical implication is that for Fred's DGP,
y(t)=0.1 + 0.1*t + y(t-1)+ e
where the 0.1*t cumulates, the adf-test option that should yield a
uniformly distributed p-value is --ctt (constant and quadratic trend).
Whoops sorry, I forgot that it actually _is_ covered then...
thanks
sven
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3 comments
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participants (3)
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Allin Cottrell -
Fred Engst -
Sven Schreiber