MySQL 8.0

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CREATE TABLE `main` (
  `event_timestamp` timestamp,
  `user_id` int(10),
  `event_name` char(12)
) DEFAULT CHARSET=utf8;
INSERT INTO `main` (`event_timestamp`, `user_id`, `event_name`) VALUES
  ('2019-01-23 20:02:21.550', '1', 'registration'),
  ('2019-01-24 20:03:21.550', '2', 'action'),
  ('2019-02-21 20:04:21.550', '3', 'registration'),
  ('2019-02-22 20:05:21.550', '4', 'registration'),
  ('2019-02-23 20:06:21.550', '5', 'registration'),
  ('2019-02-23 20:06:21.550', '1', 'action'),
  ('2019-02-24 20:07:21.550', '6', 'action'),
  ('2019-03-20 20:08:21.550', '3', 'action'),
  ('2019-03-21 20:09:21.550', '4', 'action'),
  ('2019-03-22 20:10:21.550', '9', 'action'),
  ('2019-03-23 20:11:21.550', '10', 'registration'),
  ('2019-03-22 20:10:21.550', '4', 'action'),
  ('2019-03-22 20:10:21.550', '5', 'action'),
  ('2019-03-24 20:11:21.550', '11', 'registration');
select yyyymm_reg, count(*) as regs_in_month,
       sum( month_2 > 0 ) as visits_2months,
       avg( month_2 > 0 ) as return_rate_2months
from (select m.user_id, m.yyyymm_reg,
             max( (timestampdiff(month, m.yyyymm_reg, m.yyyymm) = 1) ) as month_1,
             max( (timestampdiff(month, m.yyyymm_reg, m.yyyymm) = 2) ) as month_2,
             max( (timestampdiff(month, m.yyyymm_reg, m.yyyymm) = 3) ) as month_3
      from (select m.*,
                   cast(concat(extract(year_month from event_timestamp), '01') as date) as yyyymm,
                   cast(concat(extract(year_month from min(case when event_name = 'registration' then event_timestamp end) over (partition by user_id)), '01') as date) as yyyymm_reg
            from main m
           ) m
      where m.yyyymm_reg is not null
      group by m.user_id, m.yyyymm_reg
     ) u
group by u.yyyymm_reg;


yyyymm_reg
regs_in_month
visits_2months
return_rate_2months


2019-01-01
1
0
0.0000

2019-02-01
3
0
0.0000

2019-03-01
2
0
0.0000