How to calculate smoothed moving average using Postgres SQL - sql

Question

I have a table in my Postgresql DB that has the fields: product_id, date, sales_amount.
I am calculating a simple moving average for the last 1 week using the below SQL
SELECT date,
AVG(amount)
OVER(PARTITION BY product_id ORDER BY date ROWS BETWEEN 6 PRECEDING AND CURRENT ROW) AS avg_amount
FROM sales
How can I calculate a smoothed moving average(smma) instead the simple moving average above? I have found that the formula is smma_today = smma_yesterday * (lookback_period - 1) + amount) / lookback_period
but how to translate to SQL?
A CTE or function or query approach suggestion will be appreciated

Answer 1

I am pretty sure you will need recursion since your formula depends on using a value calculated for a previous row in the current row.
with recursive mma as (
(select distinct on (product_id) *, ddate as basedate,
amount as sm_mov_avg
from smma
order by product_id, ddate)
union all
select smma.*, mma.basedate,
( mma.sm_mov_avg
* least(smma.ddate - mma.basedate, 6)
+ smma.amount) / least(smma.ddate - mma.basedate + 1, 7)
from mma
join smma on smma.product_id = mma.product_id
and smma.ddate = mma.ddate + 1
)
select ddate, product_id, amount, round(sm_mov_avg, 2) as sm_mov_avg,
round(
avg(amount) over (partition by product_id
order by ddate
rows between 6 preceding
and current row), 2) as mov_avg
from mma;
Please note how the smooth moving average and the moving average begin to diverge after you reach the lookback of seven days:
ddate | product_id | amount | sm_mov_avg | mov_avg
:--------- | ---------: | -----: | ---------: | ------:
2020-11-01 | 1 | 8 | 8.00 | 8.00
2020-11-02 | 1 | 4 | 6.00 | 6.00
2020-11-03 | 1 | 7 | 6.33 | 6.33
2020-11-04 | 1 | 9 | 7.00 | 7.00
2020-11-05 | 1 | 4 | 6.40 | 6.40
2020-11-06 | 1 | 6 | 6.33 | 6.33
2020-11-07 | 1 | 4 | 6.00 | 6.00
2020-11-08 | 1 | 1 | 5.29 | 5.00
2020-11-09 | 1 | 8 | 5.67 | 5.57
2020-11-10 | 1 | 10 | 6.29 | 6.00
2020-11-11 | 1 | 8 | 6.54 | 5.86
2020-11-12 | 1 | 4 | 6.17 | 5.86
2020-11-13 | 1 | 3 | 5.72 | 5.43
2020-11-14 | 1 | 2 | 5.19 | 5.14
2020-11-15 | 1 | 5 | 5.16 | 5.71
2020-11-16 | 1 | 8 | 5.57 | 5.71
2020-11-17 | 1 | 4 | 5.34 | 4.86
2020-11-18 | 1 | 10 | 6.01 | 5.14
2020-11-19 | 1 | 5 | 5.86 | 5.29
2020-11-20 | 1 | 3 | 5.46 | 5.29
2020-11-21 | 1 | 3 | 5.10 | 5.43
2020-11-22 | 1 | 9 | 5.66 | 6.00
2020-11-23 | 1 | 7 | 5.85 | 5.86
2020-11-24 | 1 | 1 | 5.16 | 5.43
2020-11-25 | 1 | 10 | 5.85 | 5.43
2020-11-26 | 1 | 7 | 6.01 | 5.71
2020-11-27 | 1 | 8 | 6.30 | 6.43
2020-11-28 | 1 | 8 | 6.54 | 7.14
2020-11-29 | 1 | 1 | 5.75 | 6.00
2020-11-30 | 1 | 9 | 6.21 | 6.29
Working Fiddle

Answer 2

Many thanks for Mike Organek's answer that showed the way forward for the calculation was a recursive approach on the query. I am starting off with the simple moving average at some distant point in the past and thereafter using the smoothed average daily which has given us exactly what we needed
with recursive my_table_with_rn as
(
SELECT
product_id,
amount,
sale_date,
row_number() over (partition by product_id order by sale_date) as rn
FROM sale
where 1=1
and sale_date > '01-Jan-2018'
order by sale_date
),
rec_query(rn, product_id, amount, sale_date, smma) as
(
SELECT
rn,
product_id,
amount,
sale_date,
AVG(amount) OVER(PARTITION BY product_id ORDER BY date ROWS BETWEEN 6 PRECEDING AND CURRENT ROW) AS smma --first entry is a simple moving average to start off
from my_table_with_rn
where rn = 1
union all
select
t.rn, t.product_id, t.amount, t.sale_date,
(p.smma * (7 - 1) + amount) / 7 -- 7 is the lookback_period; formula is smma_today = smma_previous * (lookback_period - 1) + amount) / lookback_period
from rec_query p
join my_table_with_rn t on
(t.rn = p.rn + 1 AND t.product_id = p.product_id)
)
SELECT * FROM rec_query