Calculate forecast average using recursive CTE - sql-server

Question

I was trying to answer a question here, where I need to calculate a forecast of sales based on the 3 previous months which either can be actuals or forecast.
Month Actuals Forecast
1 10
2 15
3 17
4 14.00
5 15.33
6 15.44
7 14.93
Month 4 = (10+15+17)/3
Month 5 = (15+17+14)/3
Month 6 = (17+14+15.33)/3
Month 7 = (14+15.33+15.44)/3
I've been trying to do this using a recursive CTE:
;WITH cte([month],forecast) AS (
SELECT 1,CAST(10 AS DECIMAL(28,2))
UNION ALL
SELECT 2,CAST(15 AS DECIMAL(28,2))
UNION ALL
SELECT 3,CAST(17 AS DECIMAL(28,2))
UNION ALL
SELECT
[month]=[month]+1,
forecast=CAST(AVG(forecast) OVER (ORDER BY [month] ROWS BETWEEN 3 PRECEDING AND 1 PRECEDING) AS DECIMAL(28,2))
FROM
cte
WHERE
[month]<=12
)
SELECT * FROM cte WHERE month<=12;
Fiddle: http://sqlfiddle.com/#!6/9ac4a/3
But it doesn't work as expected, as It returns the following result:
| month | forecast |
|-------|----------|
| 1 | 10 |
| 2 | 15 |
| 3 | 17 |
| 4 | (null) |
| 5 | (null) |
| 6 | (null) |
| 7 | (null) |
| 8 | (null) |
| 9 | (null) |
| 10 | (null) |
| 11 | (null) |
| 12 | (null) |
| 3 | (null) |
| 4 | (null) |
| 5 | (null) |
| 6 | (null) |
| 7 | (null) |
| 8 | (null) |
| 9 | (null) |
| 10 | (null) |
| 11 | (null) |
| 12 | (null) |
| 2 | (null) |
| 3 | (null) |
| 4 | (null) |
| 5 | (null) |
| 6 | (null) |
| 7 | (null) |
| 8 | (null) |
| 9 | (null) |
| 10 | (null) |
| 11 | (null) |
| 12 | (null) |
Expected output:
| month | forecast |
|-------|----------|
| 1 | 10 |
| 2 | 15 |
| 3 | 17 |
| 4 | 14.00 |
| 5 | 15.33 |
| 6 | 15.44 |
| 7 | 14.93 |
| 8 | 15.23 |
| 9 | 15.20 |
| 10 | 15.12 |
| 11 | 15.18 |
| 12 | 15.17 |
Can someone tell me what's wrong with this query?

Answer 1

I propose something like this:
WITH T AS
(
SELECT 1 AS [month], CAST(10 AS DECIMAL(28,2)) AS [forecast], CAST(-5 AS DECIMAL(28,2)) AS three_months_ago_forecast, CAST(9 AS decimal(28,2)) AS two_months_ago_forecast, CAST(26 AS decimal(28,2)) as one_month_ago_forecast
UNION ALL
SELECT 2,CAST(15 AS DECIMAL(28,2)), CAST(9 AS decimal(28,2)), CAST(26 AS decimal(28,2)), CAST(10 AS DECIMAL(28,2))
UNION ALL
SELECT 3,CAST(17 AS DECIMAL(28,2)), CAST(26 AS decimal(28,2)), CAST(10 AS DECIMAL(28,2)), CAST(15 AS DECIMAL(28,2))
),
LT AS -- LastForecast
(
SELECT *
FROM T
WHERE [month] = 3
),
FF AS -- Future Forecast
(
SELECT *
FROM LT
UNION ALL
SELECT
FF.[month] + 1 AS [month],
CAST( (FF.forecast * 4 - FF.three_months_ago_forecast) / 3 AS decimal(28,2)) AS forecast,
FF.two_months_ago_forecast as three_months_ago_forecast,
FF.one_month_ago_forecast as two_months_ago_forecast,
FF.forecast as one_month_ago_forecast
FROM FF
WHERE
FF.[month] < 12
)
SELECT * FROM T
WHERE [month] < 3
UNION ALL
SELECT * FROM FF
Output:
+-------+----------+---------------------------+-------------------------+------------------------+
| month | forecast | three_months_ago_forecast | two_months_ago_forecast | one_month_ago_forecast |
+-------+----------+---------------------------+-------------------------+------------------------+
| 1 | 10.00 | -5.00 | 9.00 | 26.00 |
| 2 | 15.00 | 9.00 | 26.00 | 10.00 |
| 3 | 17.00 | 26.00 | 10.00 | 15.00 |
| 4 | 14.00 | 10.00 | 15.00 | 17.00 |
| 5 | 15.33 | 15.00 | 17.00 | 14.00 |
| 6 | 15.44 | 17.00 | 14.00 | 15.33 |
| 7 | 14.92 | 14.00 | 15.33 | 15.44 |
| 8 | 15.23 | 15.33 | 15.44 | 14.92 |
| 9 | 15.20 | 15.44 | 14.92 | 15.23 |
| 10 | 15.12 | 14.92 | 15.23 | 15.20 |
| 11 | 15.19 | 15.23 | 15.20 | 15.12 |
| 12 | 15.18 | 15.20 | 15.12 | 15.19 |
+-------+----------+---------------------------+-------------------------+------------------------+

Answer 2

Try this
WITH cte
AS (SELECT *
FROM (VALUES (1,10,NULL),
(2,15,NULL),
(3,17,NULL),
(4,NULL,14.00),
(5,NULL,15.33),
(6,NULL,15.44),
(7,NULL,14.93)) tc (month, act, fore))
SELECT mon,avg(res)
FROM cte a
CROSS apply (SELECT TOP 3 ( COALESCE(a.act, a.fore) ) AS res,
b.month AS mon
FROM cte b
WHERE a.month < b.month
ORDER BY a.month DESC) cs
GROUP BY mon
ORDER BY mon
or in Sql Server 2012+ use this
SELECT
[month]=[month]+1,
forecast=CAST(AVG(COALESCE(act,fore)) OVER (ORDER BY [month] ROWS BETWEEN 3 PRECEDING AND CURRENT row ) AS DECIMAL(28,2))
FROM
cte