[Gretl-users] Re: Durbin Watson p-value
Am 09.11.2020 um 13:36 schrieb Allin Cottrell:
On Mon, 9 Nov 2020, ANA JESUS LOPEZ MENENDEZ wrote:
> According to the user`s guide “an approximate P-value for the null of
> no serial correlation (rho= 0) against the alternative of rho> 0 may
> be available via the accessor $dwpval”.
>
> However when using this Gretl option it apparently provides the
> left-tail probability, for example
>
> Durbin-Watson = 1,38 p = 0,003
>
> Durbin-Watson = 2,33919 p = 0,785174
Gretl is providing what it claims to provide, namely the P-value for a
one tailed test (rho = 0 versus rho greater than zero). DW < 2
suggests rho > 0 so the small P-value you quote for DW = 1.38 looks
plausible, and the large P-value for DW = 2.34 is likewise plausible.
The reference
for the $dwpval accessor is currently silent about
one-tailed vs. two-tailed, however. I guess the formulation from the
guide should be copied over.
But if you want a two tailed test then your proposal is right.
BTW, we had a related discussion about ADF unit root test p-values. I
had pointed out that for a one-tailed test in the situation where the
test statistic falls in the H0 region (there: to the right of one, here:
to the left of zero) it is kind of inconsistent with standard inference
theory to let p<1. Or put differently, if you want to test theta = 0 vs.
theta > 0 and you return a p-value p<1 if \hat{theta} < 0, then you are
putting the H0 value theta=0 into the critical region of the test, which
doesn't make sense.
But I admit that the practical relevance is very limited if the
documentation is complete, and many other packages do it like gretl does
there.
cheers
sven