Merging multiple "state-change" time series - sql

Question

Given a number of tables like the following, representing state-changes at time t of an entity identified by id:
| A | | B |
| t | id | a | | t | id | b |
| - | -- | - | | - | -- | - |
| 0 | 1 | 1 | | 0 | 1 | 3 |
| 1 | 1 | 2 | | 2 | 1 | 2 |
| 5 | 1 | 3 | | 3 | 1 | 1 |
where t is in reality a DateTime field with millisecond precision (making discretisation infeasible), how would I go about creating the following output?
| output |
| t | id | a | b |
| - | -- | - | - |
| 0 | 1 | 1 | 3 |
| 1 | 1 | 2 | 3 |
| 2 | 1 | 2 | 2 |
| 3 | 1 | 2 | 1 |
| 5 | 1 | 3 | 1 |
The idea is that for any given input timestamp, the entire state of a selected entity can be extracted by selecting one row from the resulting table. So the latest state of each variable corresponding to any time needs to be present in each row.
I've tried various JOIN statements, but I seem to be getting nowhere.
Note that in my use case:
rows also need to be joined by entity id
there may be more than two source tables to be merged
I'm running PostgreSQL, but I will eventually translate the query to SQLAlchemy, so a pure SQLAlchemy solution would be even better
I've created a db<>fiddle with the example data.

Answer 1

I think you want a full join and some other manipulations. The ideal would be:
select t, id,
last_value(a.a ignore nulls) over (partition by id order by t) as a,
last_value(b.b ignore nulls) over (partition by id order by t) as b
from a full join
b
using (t, id);
But . . . Postgres doesn't support ignore nulls. So an alternative method is:
select t, id,
max(a) over (partition by id, grp_a) as a,
max(b) over (partition by id, grp_b) as b
from (select *,
count(a.a) over (partition by id order by t) as grp_a,
count(b.b) over (partition by id order by t) as grp_b
from a full join
b
using (t, id)
) ab;