How to sum the values of a column for several rows?

This is a gaps and islands problem. Canonical solutions do use window functions, which as far as concerns, Clickhouse does not support.

Here is one approach that uses a subquery to emulate a conditional window sum:

select
    min(date) start_date,
    max(date) end_date,
    sum(change) sum_change
from (
    select 
        t.*,
        (select count(*) from mytable t1 where t1.date <= t.date and t1.ne = 0) grp
    from mytable t
) t
group by grp

The subquery counts how many rows have ne = 0 from the first row of the table until the current row. This defines groups of records. Then all that is left to do is aggregate.

If you could use window functions, you would phrase this as:

select
    min(date) start_date,
    max(date) end_date,
    sum(change) sum_change
from (
    select 
        t.*,
        sum(case when ne = 0 then 1 else 0 end) over(order by date) grp
    from mytable t
) t
group by grp

it's unsolvable in bigdata ( > 100 millions rows)

SELECT
    d[1] AS s,
    d[-1] AS e,
    arraySum(c) AS sm
FROM
(
    SELECT
        arraySplit((x, y) -> (NOT y), d, n) AS dd,
        arraySplit((x, y) -> (NOT y), c, n) AS cc
    FROM
    (
        SELECT
            groupArray(date) AS d,
            groupArray(ne) AS n,
            groupArray(change) AS c
        FROM
        (
            SELECT *
            FROM mytable
            ORDER BY rn ASC
        )
    )
)
ARRAY JOIN
    dd AS d,
    cc AS c

┌─s──────────┬─e──────────┬───────────sm─┐
│ 2008-12-07 │ 2009-04-26 │   -725166328 │
│ 2013-07-06 │ 2015-06-08 │ -15224653176 │
└────────────┴────────────┴──────────────┘

Just another way to resolve this task:

WITH (SELECT arraySort(groupArray(rn))
    FROM test_table
    WHERE ne = 0) as group_start_id
SELECT argMin(date, rn) start, argMax(date, rn) end, sum(change)
FROM (
    SELECT rn, date, change
    FROM test_table
    ORDER BY rn)
GROUP BY arrayFirstIndex(x -> rn < x, group_start_id)   
ORDER BY start

Testing on sample data:

WITH (SELECT arraySort(groupArray(rn))
    FROM (
        SELECT data.1 rn, data.2 date, data.3 ne, data.4 change
        FROM (
            SELECT arrayJoin([
            (0, toDate('2008-12-07'), 0, toInt64(-10330848398)),
            (1, toDate('2009-04-14'), 1, toInt64(-61290)),
            (2, toDate('2009-04-26'), 1, toInt64(9605743360)),
            (3, toDate('2013-07-06'), 0, toInt64(-32028871920)),
            (4, toDate('2014-01-12'), 1, toInt64(-42296164902)),
            (5, toDate('2015-06-08'), 1, toInt64(59100383646)),
            (6, toDate('2015-06-08'), 0, toInt64(101)),
            (7, toDate('2015-06-09'), 0, toInt64(102)),
            (8, toDate('2015-06-10'), 0, toInt64(103)),
            (9, toDate('2015-06-11'), 1, toInt64(104))
            ]) data))
    WHERE ne = 0) as group_start_id
SELECT argMin(date, rn) start, argMax(date, rn) end, sum(change)
FROM (
    SELECT data.1 rn, data.2 date, data.4 change
    FROM (
        SELECT arrayJoin([
        (0, toDate('2008-12-07'), 0, toInt64(-10330848398)),
        (1, toDate('2009-04-14'), 1, toInt64(-61290)),
        (2, toDate('2009-04-26'), 1, toInt64(9605743360)),
        (3, toDate('2013-07-06'), 0, toInt64(-32028871920)),
        (4, toDate('2014-01-12'), 1, toInt64(-42296164902)),
        (5, toDate('2015-06-08'), 1, toInt64(59100383646)),
        (6, toDate('2015-06-08'), 0, toInt64(101)),
        (7, toDate('2015-06-09'), 0, toInt64(102)),
        (8, toDate('2015-06-10'), 0, toInt64(103)),
        (9, toDate('2015-06-11'), 1, toInt64(104))
        ]) data)
    ORDER BY rn)
GROUP BY arrayFirstIndex(x -> rn < x, group_start_id)   
ORDER BY start
/* result
┌──────start─┬────────end─┬──sum(change)─┐
│ 2008-12-07 │ 2009-04-26 │   -725166328 │
│ 2013-07-06 │ 2015-06-08 │ -15224653176 │
│ 2015-06-08 │ 2015-06-08 │          101 │
│ 2015-06-09 │ 2015-06-09 │          102 │
│ 2015-06-10 │ 2015-06-11 │          207 │
└────────────┴────────────┴──────────────┘
*/

SELECT ne, MIN(date) as start, MAX(date) as end, SUM(change) as change GROUP BY ne

Assuming Clickhouse supports variables:

set @block := -1;
select 
    block as row,
    min(date) as start,
    max(date) as end,
    sum(change)
from
    (select  
        case when ne = 0 then @block:=@block+1 end as dummy,
        @block as block,
        t.*
    from t) tt
group by block;