[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 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