# Replicating Dickey Fuller? How did they know something was wrong? [cross posted on QF] [on hold]

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-posted to QF

## put on hold as off-topic by gung♦yesterday

• This question does not appear to be about statistics within the scope defined in the help center.
If this question can be reworded to fit the rules in the help center, please edit the question.

• Please do not cross-post. Pick the site where you want your question to be & delete the other version. – gung yesterday
• I'm voting to close this question as off-topic because it is cross-posted on Quantitative Finance. – gung yesterday