Cross sectional T-test, event-study

Hello, I'm new to the forum and I have tried searching for it but couldn't quite find my solution.

I'm working on a paper involving an Event study about CEO turnovers through the years of 2002-2013. By calculating the abnormal returns and using estimations windows and event windows I'm getting results for my single mean t-test. However not really significant results. That why I want to do further testing, also for robustness

I'm trying the replicate the paper of Kind&Schlaepfer, where they use the cross-sectional T-test by the paper of Boehmer, Musumeci and Poulsen "Event-study methodoly under conditions of event-induced variance."

What I'm not getting in their formula(I looked up different papers for this) for their getting their standarized residuals, when I have my Abnormal returns and cumulative abnormal returns what should I regress to get these? I'm really kind of lost here.

Next to this I also found another formula, where I need to use the standard deviation, but adjusted by the forecast error, if I could probably get this standard deviation I can calculate the cross sectional t-test using Excel(preferably STATA, however being lost in there with all the formula's, no thanks.

To sum up, how to get standarized residuals(what to regress with only abnormal returns?)
Or else, how to get standard deviation adjust for forecast errors.

I really hope you get what I'm trying to do here and that you guys can help me out.

Thank you! :)