SQL Server window functions: building up a history string - sql

Question

I have a table of longitudinal data that looks like this:
where id is the partition variable, period is the time dimension, and val is the observation value.
I want to build up a history of val for each panel of id, like this:
I'm trying to do this with SQL window functions and not a cursor, but the issue I keep running into is the self-referential nature of the hist column definition. It almost seems like I'd have to create one row/column per period. For example, the closest I could come was this:
IF OBJECT_ID('dbo.my_try', 'U') IS NOT NULL
DROP TABLE dbo.my_try;
GO
SELECT
id, period, val,
CASE
WHEN (
period = MIN(period)
OVER (PARTITION by id order by period ROWS
BETWEEN UNBOUNDED PRECEDING AND UNBOUNDED FOLLOWING)
) THEN CAST (val AS VARCHAR(60))
ELSE NULL
END AS hist
INTO my_try
FROM my_test
SELECT
id, period, val,
CASE
WHEN (
period = MIN(period) OVER
(PARTITION by id order by period ROWS
BETWEEN UNBOUNDED PRECEDING AND UNBOUNDED FOLLOWING)
) THEN hist
ELSE (
CONCAT(
val, ' | ', LAG(hist, 1) OVER (PARTITION by id order by period)
)
)
END AS hist2
FROM my_try
I would have to spool out the iteration and do a hist3, etc. for it to finally work.
Is it possible to accomplish this with SQL window functions, or is cursor the only route?
Sample Data
Here is some code to generate the original table:
CREATE TABLE my_test (
id INT,
period INT,
val INT
)
BEGIN
DECLARE #id INT = 1;
DECLARE #period INT = 1;
WHILE #id <= 3
BEGIN
SET #period = 1
WHILE #period <= 3
BEGIN
INSERT INTO my_test VALUES (#id, #period, #period * POWER(10, #id))
SET #period = #period + 1
END
SET #id = #id + 1
END
END

Answer 1

Actually you don't need recursion here. You can leverage STUFF pretty easily. Of course if you are on 2017 you can use string_agg as suggested above. But if you are like me and your company is not the fastest to adopt the latest and greatest you can use this.
select t1.id
, t1.period
, t1.val
, STUFF((select ' | ' + convert(varchar(10), val)
from my_test t2
where t2.id = t1.id
and t2.period <= t1.period
order by t1.period
FOR XML PATH('')), 1, 3,'')
from my_test t1
order by t1.id
, t1.period

Answer 2

As discussed in the comments try using recursive query
with cte as(
select id, [period], val, convert(varchar(max), val) as agg from my_try where [period] = 1
union all
select t.id, t.[period], t.val, CONCAT(c.agg, ' | ', t.val) from my_try t join cte c on c.[period] +1 = t.[period] and c.id = t.id
)
select * from cte order by id, [period]