I'm currently working with financial time series that experience a crash towards the middle of the series. These series are returns. From the graph, these series clearly look stationary. However, due to there being a crash, there is a bit of auto-correlation around the crash. Performing unit root tests on the whole series do not allow me to reject the hypothesis of a unit root, I'm fairly certain this is due to the crash which lasts a bit.
Can I perform the unit root tests on the series taking out the observations of the crash and then, if I can reject the hypothesis of a unit root, argue the whole series is in fact stationary, there was just a large crash that made it seem non-stationary.
Otherwise, do you have any suggestion of how to implement a unit root test with a dummy for the time of the crash? I imagine the critical values would change.