SQL Server : Using LAG() with calculated previous value

This is gaps and island problem where each non-zero value marks the beginning of a new island. Once grouped you can use first_value to pick out the corresponding "previous value" while row_number serves as an offset for computing a multiplier.

with A as (
    select *,
      sum(case when "value" <> 0 then 1 else 0 end)
        over (order by periode_forecast) as grp
    from T
), B as (
    select *,
      first_value("value")
        over (partition by grp order by periode_forecast) as pv,
      power(10e, 1 - row_number()
        over (partition by grp order by periode_forecast)) as mult
    from A
)
select periode_forecast, "value", grp, pv, pv * mult as new_value
from B
order by periode_forecast;

You may want to stick with decimal math and avoid float. If so then adjust the 10e inside the power() reference.

If there is no valid prior non-zero row then the result will be zero. It's not clear whether that will happen in your data or how to treat it differently.

https://dbfiddle.uk/?rdbms=sqlserver_2016&fiddle=545d6e84ea43885788e45a2fb0393884

Your problem is that you lag the value 0 when you are 2 month after the first periode. I think that you have to use a parameter for the second part of the function lag(). Someting like : lag(VALUE, DATEDIFF(m,convert(date,'2021-08-01'),convert(date,'2021-10-01')) ,0 )

here :

Lag( Value, DATEDIFF(m,convert(date,PERIODE),convert(date,PERIODE_FORECAST)) ,0 )

You maybe have to add this datediff as exponent for the multiplicator 0.1.

This was an interesting question, and my approach is likely not the most performant since I am a programmer, but it does produce the results you expect. I first create a common table expression and number the rows with ROW_NUMBER. Then I join back to the CTE to find the single VALUE with the highest ROW_NUMBER. You can this use the difference in ROW_NUMBERs as a POWER of 10.0000 to get the multiplier.

First I created your data:

DECLARE @Forecast AS TABLE
(
    [PERIODE]          DATE           NOT NULL,
    [PERIODE_FORECAST] DATE           NOT NULL,
    [VALUE]            DECIMAL(16, 8) NOT NULL
);

INSERT INTO @Forecast
(
    [PERIODE],
    [PERIODE_FORECAST],
    [VALUE]
)
VALUES
('2021-08-01', '2021-01-01', 51384.673),
('2021-08-01', '2021-02-01', 44118.129),
('2021-08-01', '2021-03-01', 43164.446),
('2021-08-01', '2021-04-01', 38113.745),
('2021-08-01', '2021-05-01', 37306.956),
('2021-08-01', '2021-06-01', 38390.359),
('2021-08-01', '2021-07-01', 42692.390),
('2021-08-01', '2021-08-01', 39814.047),
('2021-08-01', '2021-09-01', 0.000),
('2021-08-01', '2021-10-01', 0.000),
('2021-08-01', '2021-11-01', 0.000),
('2021-08-01', '2021-12-01', 0.000);

Once I had this, the query is:

;WITH [NumberedRows]
AS (SELECT [PERIODE],
           [PERIODE_FORECAST],
           [VALUE],
           ROW_NUMBER() OVER (PARTITION BY [PERIODE]
                              ORDER BY [PERIODE_FORECAST]
                             ) AS [rn]
    FROM   @Forecast)
SELECT [nr1].[PERIODE],
       [nr1].[PERIODE_FORECAST],
       CASE WHEN [sub].[VALUE] IS NOT NULL THEN
                [sub].[VALUE] * POWER(10.0000000, ([sub].[rn] - [nr1].[rn]))
            ELSE
                [nr1].[VALUE]
       END AS [VALUE]
FROM   [NumberedRows] AS [nr1]
       LEFT OUTER JOIN
       (
           SELECT   TOP(1)
                    [nr2].[PERIODE], [nr2].[PERIODE_FORECAST], [nr2].[VALUE], [nr2].[rn]
           FROM     [NumberedRows] [nr2]
           WHERE    [nr2].[VALUE] <> 0
           ORDER BY [nr2].[rn] DESC
       ) AS [sub]
           ON [sub].[PERIODE] = [nr1].[PERIODE]
              AND [sub].[rn] < [nr1].[rn];

And the results: