[Gretl-users] Re: 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