# How did Dickey and Fuller know something was wrong?

I am interested in testing if there is size distortion through simulations. I have recently been interested in replicating Dickey and Fuller (1979) and this source from another post helped a lot, here

However, whilst they are generating the correct critical values, how did Dickey and Fuller know that something was wrong in the first place.

From my understanding, the premise of the argument is the the t distribution was not effective when computing hypotheses tests when the AR(1) coefficient was 1, i.e.,

$$Y_t=\delta+Y_{t-1}+\varepsilon_t$$

So my question is, how would I go about simulating some data and testing the level of size distortion?

Whilst this may seem trivial for the DF research I would like to be able to understand this for a more complicated framework so any advice would be appreciated?

Cross post 2

• Could you show on CV that the question is cross-posted here? Given the time of year an answer might take more than a week but you're right that it didn't attract much attention on CV so let's try. – Bob Jansen Jan 14 '19 at 13:55
• stats.stackexchange.com/questions/386118/… – user22485 Jan 14 '19 at 14:02