I am looking for literature that suggests the augmented Dickey-Fuller (ADF) test is not completely accurate, or in general criticizing the test.
There are various criticisms, some of which, in my opinion, are more pertinent than others:
- Lack of power: When testing $\rho=1$ against $|\rho|<1$, it is argued that many macroeconomic time series may be expected to be well-described by a $\rho$ close to, but less than 1. The test lacks power to detect this. To some extent, that criticism is invalid, because all tests have low power when the actual parameter value is close to the null value. To some extent, it is valid because there are tests that apply under broader sets of assumptions, or are simply more powerful than the ADF test.
- Size distortion: as for most tests, the null distribution is only available asymptotically, and the finite-sample distribution is often argued to differ substantially from the asymptotic one, leading to actual rejection rates that differ substantially from the nominal level $\alpha$.
- General scepticism towards the usefulness of testing point null hypotheses, fairly common among Bayesian statisticians.