SQL Mean Absolute Deviation - sql

Question

I am attempting to calculate the "Mean Absolute Deviation" from the following SQL Table:
|ID | Typical | SMA | MAD
| 1 | 10 | |
| 2 | 20 | |
| 3 | 5 | 11.67 |
| 4 | 12 | 12.33 |
| 5 | 14 | 10.33 |
| 6 | 6 | 10.67 |
| 7 | 2 | 7.33 |
| 8 | 17 | 8.33 |
| 9 | 5 | 8.00 |
Calculating the MAD requires:
SUM ( ABS( Current Row SMA - Typical)) Over the Previous 2 rows and current. This is then divided by 3. So for ID #3 it would be:
MAD = (ABS(11.67 - 5) + ABS(11.67 - 20) + ABS(11.67 - 10)) / 3
I first did this with Dyamic SQL, looping through and creating a LAG for each previous row. This works, but is very inefficient when its scaled up to a higher lookback period. I then attempted the below which I really thought would work, but did not:
DECLARE #sma_current numeric(20,10)
UPDATE PY SET
#sma_current = [SMA(20)],
[MAD] = W.[MAD]
FROM (
SELECT [id],
((sum(abs(#sma_current - [Typical])) OVER (ORDER BY [id] ASC ROWS
BETWEEN 2 PRECEDING AND CURRENT ROW))/3) [MAD]
FROM PY ) W WHERE PY.[id] = W.[id] AND PY.[id] >= 3
Any help would be greatly appreciated.

Answer 1

Since the ids are sequential and there are no gaps you can do the update with a double self join:
update p
set p.mad = round(
(abs(p.sma - p.typical) + abs(p.sma - p1.typical) + abs(p.sma - p2.typical)) / 3.0
, 2)
from py p
inner join py p1 on p1.id + 1 = p.id
inner join py p2 on p2.id + 2 = p.id
See the demo.
Or with lag() window function:
with cte as (
select *,
lag(typical, 1) over (order by id) typical1,
lag(typical, 2) over (order by id) typical2
from py
)
update cte
set mad = round(
(abs(sma - typical) + abs(sma - typical1) + abs(sma - typical2)) / 3.0
, 2)
from cte
See the demo.
Results:
> ID | Typical | SMA | MAD
> -: | ------: | ----: | ---:
> 1 | 10 | |
> 2 | 20 | |
> 3 | 5 | 11.67 | 5.56
> 4 | 12 | 12.33 | 5.11
> 5 | 14 | 10.33 | 3.56
> 6 | 6 | 10.67 | 3.11
> 7 | 2 | 7.33 | 4.44
> 8 | 17 | 8.33 | 5.78
> 9 | 5 | 8 | 6

Answer 2

I am guessing that you are using SQL Server. You can use an updatable CTE/subquery so do the calculation there and then set it:
WITH toupdate as (
SELECT id,
(sum(abs(#sma_current - [Typical])) OVER (ORDER BY [id] ASC ROWS BETWEEN 2 PRECEDING AND CURRENT ROW) / 3) as new_mad
FROM PY
)
UPDATE toupdate
SET mad = new_mad;