Annualized standard deviation from quarterly data and logistic distribution for probability of Yt+1

[Sofi Gomes]

Hello,

My data looks like this:

id	t	bankruptcy_dummy	income	return
1	1	0	0.5	0.1
1	2	0	0.7	0.13
1	3	1	.	.
1	4	.	.	.
1	5	.	.	.
1	...	.	.	.
2	1	0	0.78	0.2
2	2	0	0.34	0.24
2	...	0	...	...

Each t represents one quarter and t goes from 1 to 40, thus periods 1 to 4 make the first year and 37 to 40 make year ten.
Whenever a firm (i.e., id) disappears from the dataset, I have a ".".

My questions are regarding two things:

Firstly, I need to create a variable sigma for annualized rolling standard deviation of returns. I am having trouble doing this. All the solutions I have found so far are for cases when people have the date (e.g. "31Jan2013") in t. I honestly have no idea which functions should I use here.

Secondly, the point of my study is to see if my variables impact the probability of bankruptcy in the next period, and this probability follows a logistic distribution.

I am not sure how to do this. So, by parts:

• By executing gen bnkr1 = bnkr[_n+1] I would get Y_t+1? Or should I somehow do the opposite and lag my explanatory variables?
• Then, could I create a vector x by executing global xlist income return sigma
• Then how do I build the probability? I know it follows a logistic distribution, so I guess I would use logit(xlist) maybe?
• Finally, how do I regress considering this probability? reg bnkr1 xlist wouldn't take into account this logistic distribution...

Thank you in advance!

[Sofi Gomes]

Update:

I still haven't managed the rolling standard deviation, but I tried the logit regression bit and got all failures, so I would really appreciate some help regarding in what I might have failed.

I did the following:

• gen bnkr1 = bnkr[_n+1]
• then global id id
• global t t
• global ylist bnkrq
• global xlist income (other indep variables)
• then sort $id $t
• xtset $id $t
• xtdescribe
• xtsum $id $t $ylist $xlist
• and finally logit $ylist $xlist