How to get interpolation value in SQL Server? - sql

Question

I want to get interpolation value for NULL. Interpolation is a statistical method by which related known values are used to estimate an unknown price or potential yield of a security. Interpolation is achieved by using other established values that are located in sequence with the unknown value.
Here is my sample table and code.
https://dbfiddle.uk/?rdbms=sqlserver_2017&fiddle=673fcd5bc250bd272e8b6da3d0eddb90
I want to get this result:
| SEQ | cat01 | cat02 | dt_day | price | coeff |
+-----+-------+-------+------------+-------+--------+
| 1 | 230 | 1 | 2019-01-01 | 16000 | 0 |
| 2 | 230 | 1 | 2019-01-02 | NULL | 1 |
| 3 | 230 | 1 | 2019-01-03 | 13000 | 0 |
| 4 | 230 | 1 | 2019-01-04 | NULL | 1 |
| 5 | 230 | 1 | 2019-01-05 | NULL | 2 |
| 6 | 230 | 1 | 2019-01-06 | NULL | 3 |
| 7 | 230 | 1 | 2019-01-07 | 19000 | 0 |
| 8 | 230 | 1 | 2019-01-08 | 20000 | 0 |
| 9 | 230 | 1 | 2019-01-09 | 21500 | 0 |
| 10 | 230 | 1 | 2019-01-10 | 21500 | 0 |
| 11 | 230 | 1 | 2019-01-11 | NULL | 1 |
| 12 | 230 | 1 | 2019-01-12 | NULL | 2 |
| 13 | 230 | 1 | 2019-01-13 | 23000 | 0 |
| 1 | 230 | 2 | 2019-01-01 | NULL | 1 |
| 2 | 230 | 2 | 2019-01-02 | NULL | 2 |
| 3 | 230 | 2 | 2019-01-03 | 12000 | 0 |
| 4 | 230 | 2 | 2019-01-04 | 17000 | 0 |
| 5 | 230 | 2 | 2019-01-05 | 22000 | 0 |
| 6 | 230 | 2 | 2019-01-06 | NULL | 1 |
| 7 | 230 | 2 | 2019-01-07 | 23000 | 0 |
| 8 | 230 | 2 | 2019-01-08 | 23200 | 0 |
| 9 | 230 | 2 | 2019-01-09 | NULL | 1 |
| 10 | 230 | 2 | 2019-01-10 | NULL | 2 |
| 11 | 230 | 2 | 2019-01-11 | NULL | 3 |
| 12 | 230 | 2 | 2019-01-12 | NULL | 4 |
| 13 | 230 | 2 | 2019-01-13 | 23000 | 0 |
I use this code. I think this code incorrect.
coeff is the NULL is in order set.
This code is for implementing interpolation.
I tried to find out between the empty values and divide them by the number of spaces.
But, this code is incorrect.
WITH ROW_VALUE AS
(
SELECT SEQ
, dt_day
, cat01
, cat02
, price
, ROW_NUMBER() OVER (ORDER BY dt_day) AS sub_seq
FROM (
SELECT SEQ
, cat01
, cat02
, dt_day
, dt_week
, dt_month
, price
FROM temp01
WHERE price IS NOT NULL
)val
)
,STEP_CHANGE AS(
SELECT RV1.SEQ AS id_Start
, RV1.SEQ - 1 AS id_End
, RV1.cat01
, RV1.cat02
, RV1.dt_day
, RV1.price
, (RV2.price - RV1.price)/(RV2.SEQ - RV1.SEQ) AS change1
FROM ROW_VALUE RV1
LEFT JOIN ROW_VALUE RV2 ON RV1.cat01 = RV2.cat01
AND RV1.cat02 = RV2.cat02
AND RV1.SEQ = RV2.SEQ - 1
)
SELECT *
FROM STEP_CHANGE
ORDER BY cat01, cat02, dt_day
Please, let me know what a good way to fill NULL using linear relationships.
If there is another good way, please recommend it.

Answer 1

If I assume that you mean linear interpolation between the previous price and the next price based on the number of days that passed, then you can use the following method:
Use window functions to get the next and previous days with prices for each row.
Use window functions or joins to get the prices on those days as well.
Use arithmetic to calculate the linear interpolation.
You SQL Fiddle uses SQL Server, so I assume that is the database you are using. The code looks like this:
select t.*,
coalesce(t.price,
(tprev.price +
(tnext.price - tprev.price) / datediff(day, prev_price_day, next_price_day) *
datediff(day, t.prev_price_day, t.dt_day)
)
) as imputed_price
from (select t.*,
max(case when price is not null then dt_day end) over (partition by cat01, cat02 order by dt_day asc) as prev_price_day,
min(case when price is not null then dt_day end) over (partition by cat01, cat02 order by dt_day desc) as next_price_day
from temp01 t
) t left join
temp01 tprev
on tprev.cat01 = t.cat01 and
tprev.cat02 = t.cat02 and
tprev.dt_day = t.prev_price_day left join
temp01 tnext
on tnext.cat01 = t.cat01 and
tnext.cat02 = t.cat02 and
tnext.dt_day = t.next_price_day
order by cat01, cat02, dt_day;
Here is a db<>fiddle.