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Utworzyłem tsrange_interception_agg agregat

create function tsrange_interception (
    internal_state tsrange, next_data_values tsrange
) returns tsrange as $$
    select internal_state * next_data_values;
$$ language sql;

create aggregate tsrange_interception_agg (tsrange) (
    sfunc = tsrange_interception,
    stype = tsrange,
    initcond = $$[-infinity, infinity]$$
);

Następnie to zapytanie

with td (id, begin_time, end_time) as
(
    values
    (1, '2014-01-01'::timestamp, '2014-01-31'::timestamp),
    (1, '2014-02-01', '2014-02-28'),
    (1, '2014-04-01', '2014-04-30'),
    (2, '2014-01-15', '2014-02-20'),
    (2, '2014-04-15', '2014-05-05'),
    (3, '2014-01-20', '2014-04-20')
), ranges as (
    select
        id,
        row_number() over(partition by id) as rn,
        tsrange(begin_time, end_time) as tr
    from td
), cr as (
    select r0.tr tr0, r1.tr as tr1
    from ranges r0 cross join ranges r1
    where
        r0.id < r1.id and
        r0.tr && r1.tr and
        r0.id = (select min(id) from td)
)
select tr0 * tsrange_interception_agg(tr1) as interseptions
from cr
group by tr0
having count(*) = (select count(distinct id) from td) - 1
;
                 interseptions                 
-----------------------------------------------
 ["2014-02-01 00:00:00","2014-02-20 00:00:00")
 ["2014-01-20 00:00:00","2014-01-31 00:00:00")
 ["2014-04-15 00:00:00","2014-04-20 00:00:00")