Continuously arriving data with fast filtering on date in PostgreSQL
As @a_horse_with_no_name suggested, you could do partitioning of the tables, which seems ideal for what you are describing. Something like pg_partman would help significantly with the process:

https://github.com/keithf4/pg_partman

You could also try an unlogged table, with a job to load the table in between bursts, something like this:

http://theplateisbad.blogspot.com/2015/08/row-row-row-your-boat.html

But in the end, I think that partitioning is the best way to go here, so that you are writing to a smaller table with many other sibling tables, the table inheritance is hidden behind PostgreSQL's partitioning machinery, and entire partitions can be eliminated via constraint exclusion depending on timestamp ranges.