So you just want a normal running total and then filter the results?
If so, first calculate the whole total, then apply your restrictions in an outer query:
select * from (
select t.*,
sum(amt) over (
order by dt
) tot
from t
)
where dt >= date'2016-10-03'
order by dt desc;
ID DT AMT TOT
---------- --------- ---------- ----------
4 04-OCT-16 20 160
3 03-OCT-16 -10 140
Note this requires you to scan the whole data set before filtering. So this could be slow if you're calculating the total over a large number of transactions.