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