SQL interpolating missing values for a specific date range - with some conditions - sql

Question

There are some similar questions on the site, but I believe mine warrants a new post because there are specific conditions that need to be incorporated.
I have a table with monthly intervals, structured like this:
+----+--------+--------------+--------------+
| ID | amount | interval_beg | interval_end |
+----+--------+--------------+--------------+
| 1 | 10 | 12/17/2017 | 1/17/2018 |
| 1 | 10 | 1/18/2018 | 2/18/2018 |
| 1 | 10 | 2/19/2018 | 3/19/2018 |
| 1 | 10 | 3/20/2018 | 4/20/2018 |
| 1 | 10 | 4/21/2018 | 5/21/2018 |
+----+--------+--------------+--------------+
I've found that sometimes there is a month of data missing around the end/beginning of the year where I know it should exist, like this:
+----+--------+--------------+--------------+
| ID | amount | interval_beg | interval_end |
+----+--------+--------------+--------------+
| 2 | 10 | 10/14/2018 | 11/14/2018 |
| 2 | 10 | 11/15/2018 | 12/15/2018 |
| 2 | 10 | 1/17/2019 | 2/17/2019 |
| 2 | 10 | 2/18/2019 | 3/18/2019 |
| 2 | 10 | 3/19/2019 | 4/19/2019 |
+----+--------+--------------+--------------+
What I need is a statement that will:
Identify where this year-end period is missing (but not find missing
months that aren't at the beginning/end of the year).
Create this interval by using the length of an existing interval for
that ID (maybe using the mean interval length for the ID to do it?). I could create the interval from the "gap" between the previous and next interval, except that won't work if I'm missing an interval at the beginning or end of the ID's record (i.e. if the record starts at say 1/16/2015, I need the amount for 12/15/2014-1/15/2015
Interpolate an 'amount' for this interval using the mean daily
'amount' from the closest existing interval.
The end result for the sample above should look like:
+----+--------+--------------+--------------+
| ID | amount | interval_beg | interval_end |
+----+--------+--------------+--------------+
| 2 | 10 | 10/14/2018 | 11/14/2018 |
| 2 | 10 | 11/15/2018 | 12/15/2018 |
| 2 | 10 | 12/16/2018 | 1/16/2018 |
| 2 | 10 | 1/17/2019 | 2/17/2019 |
| 2 | 10 | 2/18/2019 | 3/18/2019 |
+----+--------+--------------+--------------+
A 'nice to have' would be a flag indicating that this value is interpolated.
Is there a way to do this efficiently in SQL? I have written a solution in SAS, but have a need to move it to SQL, and my SAS solution is very inefficient (optimization isn't a goal, so any statement that does what I need is fantastic).
EDIT: I've made an SQLFiddle with my example table here:
http://sqlfiddle.com/#!18/8b16d

Answer 1

You can use a sequence of CTEs to build up the data for the missing periods. In this query, the first CTE (EOYS) generates all the end-of-year dates (YYYY-12-31) relevant to the table; the second (INTERVALS) the average interval length for each ID and the third (MISSING) attempts to find start (from t2) and end (from t3) dates of adjoining intervals for any missing (indicated by t1.ID IS NULL) end-of-year interval. The output of this CTE is then used in an INSERT ... SELECT query to add missing interval records to the table, generating missing dates by adding/subtracting the interval length to the end/start date of the adjacent interval as necessary.
First though we add the interp column to indicate if a row was interpolated:
ALTER TABLE Table1 ADD interp TINYINT NOT NULL DEFAULT 0;
This sets interp to 0 for all existing rows. Then we can do the INSERT, setting interp for all those rows to 1:
WITH EOYS AS (
SELECT DISTINCT DATEFROMPARTS(DATEPART(YEAR, interval_beg), 12, 31) AS eoy
FROM Table1
),
INTERVALS AS (
SELECT ID, AVG(DATEDIFF(DAY, interval_beg, interval_end)) AS interval_len
FROM Table1
GROUP BY ID
),
MISSING AS (
SELECT e.eoy,
ids.ID,
i.interval_len,
COALESCE(t2.amount, t3.amount) AS amount,
DATEADD(DAY, 1, t2.interval_end) AS interval_beg,
DATEADD(DAY, -1, t3.interval_beg) AS interval_end
FROM EOYS e
CROSS JOIN (SELECT DISTINCT ID FROM Table1) ids
JOIN INTERVALS i ON i.ID = ids.ID
LEFT JOIN Table1 t1 ON ids.ID = t1.ID
AND e.eoy BETWEEN t1.interval_beg AND t1.interval_end
LEFT JOIN Table1 t2 ON ids.ID = t2.ID
AND DATEADD(MONTH, -1, e.eoy) BETWEEN t2.interval_beg AND t2.interval_end
LEFT JOIN Table1 t3 ON ids.ID = t3.ID
AND DATEADD(MONTH, 1, e.eoy) BETWEEN t3.interval_beg AND t3.interval_end
WHERE t1.ID IS NULL
)
INSERT INTO Table1 (ID, amount, interval_beg, interval_end, interp)
SELECT ID,
amount,
COALESCE(interval_beg, DATEADD(DAY, -interval_len, interval_end)) AS interval_beg,
COALESCE(interval_end, DATEADD(DAY, interval_len, interval_beg)) AS interval_end,
1 AS interp
FROM MISSING
This adds the following rows to the table:
ID amount interval_beg interval_end interp
2 10 2017-12-05 2018-01-04 1
2 10 2018-12-16 2019-01-16 1
2 10 2019-12-28 2020-01-27 1
Demo on SQLFiddle