PostgreSQL optimization: average over range of dates - postgresql

Question

I have a query (with a subquery) that calculates an average of temperatures over the previous years, plus/minus one week per each day. It works, but it is not all that fast. The time series values below are just an example. Why I'm using doy is because I want a sliding window around the same date for every year.
SELECT days,
(SELECT avg(temperature)
FROM temperatures
WHERE site_id = ? AND
extract(doy FROM timestamp) BETWEEN
extract(doy FROM days) - 7 AND extract(doy FROM days) + 7
) AS temperature
FROM generate_series('2017-05-01'::date, '2017-08-31'::date, interval '1 day') days
So my question is, could this query somehow be improved? I was thinking about using some kind of window function or possibly lag and lead. However at least regular window functions only work on specific amount of rows, whereas there can be any number of measurements within the two-week window.
I can live with what I have for now, but as the amount of data grows so does the execution speed of the query. The two latter extracts could be removed, but that has no noticeable speed improvement and only makes the query less legible. Any help would be greatly appreciated.

Answer 1

The best index for your original query is
create index idx_temperatures_site_id_timestamp_doy
on temperatures(site_id, extract(doy from timestamp));
This can greatly improve your original query's performance.
While your original query is simple & readable, it has 1 flaw: it will calculate every day's average 14 times (on average). Instead, you could calculate these averages on a daily basis & calculate the 2 week window's weighted average (the weight for a day's average needs to be count of the individual rows in your original table). Something like this:
with p as (
select timestamp '2017-05-01' min,
timestamp '2017-08-31' max
)
select t.*
from p
cross join (select days, sum(sum(temperature)) over pn1week / sum(count(temperature)) over pn1week
from p
cross join generate_series(min - interval '1 week', max + interval '1 week', interval '1 day') days
left join temperatures on site_id = ? and extract(doy from timestamp) = extract(doy from days)
group by days
window pn1week as (order by days rows between 7 preceding and 7 following)) t
where days between min and max
order by days
However, there is not much gain here, as this is only twice as fast as your original query (with the optimal index).
http://rextester.com/JCAG41071
Notes: I used timestamp because I assumed your column's type is timestamp. But as it turned out, you use timestamptz (aka. timestamp with time zone). With that type, you cannot index the extract(doy from timestamp) expression, because that expression's output is dependent of the actual client's time zone setting.
For timestamptz use an index which (at least) starts with site_id. Using the window version should improve the performance anyway.
http://rextester.com/XTJSM42954