[Gretl-users] Re: 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