Median with a sliding window

The goal is to use MEDIAN as a window function with a sliding window of a specific size.

SELECT *,
      MEDIAN(n) OVER(ORDER BY id ROWS BETWEEN 3 PRECEDING AND CURRENT ROW)
FROM test_data
ORDER BY id;

Sliding window frame unsupported for function MEDIAN

For sample data:

CREATE OR REPLACE TEMP TABLE test_data
AS
SELECT index AS id, ABS(RANDOM(5))%100 AS n
FROM TABLE(FLATTEN(ARRAY_GENERATE_RANGE(1,10)));

The expected output for a sliding window of size 4 is:

Seeking for SQL only approach.

Median with a sliding window can be emulated by using ARRAY_AGG, ARRAY_SORT and choosing the "middle" value:

SELECT *, 
  ARRAY_SORT(ARRAY_AGG(n) OVER(ORDER BY id ROWS BETWEEN 3 PRECEDING AND CURRENT ROW)) AS sorted_arr,
  CASE WHEN ARRAY_SIZE(sorted_arr) % 2 = 1 THEN sorted_arr[FLOOR(ARRAY_SIZE(sorted_arr)/2)]::FLOAT
       ELSE (sorted_arr[ARRAY_SIZE(sorted_arr)/2-1]::FLOAT + sorted_arr[ARRAY_SIZE(sorted_arr)/2]::FLOAT)/2
  END AS median
FROM test_data
ORDER BY id;

For clarity cumulative_arr and sorted_arr presented as separate steps:

SELECT *, 
  ARRAY_AGG(n) OVER(ORDER BY id ROWS BETWEEN 3 PRECEDING AND CURRENT ROW) AS cumulative_arr,
  ARRAY_SORT(cumulative_arr) AS sorted_arr,
  CASE WHEN ARRAY_SIZE(sorted_arr)%2=1 THEN sorted_arr[FLOOR(ARRAY_SIZE(sorted_arr)/2)]::FLOAT
       ELSE (sorted_arr[ARRAY_SIZE(sorted_arr)/2-1]::FLOAT + sorted_arr[ARRAY_SIZE(sorted_arr)/2]::FLOAT)/2
    END AS median
FROM test_data
ORDER BY id;

Output: