MySQL 8.0

By using db<>fiddle, you agree to license everything you submit by Creative Commons CC0.
CREATE TABLE IF NOT EXISTS `test`
(
   `date_time` DATETIME UNIQUE NOT NULL,
   `data` INT NOT NULL
)
ENGINE InnoDB;
INSERT INTO `test` VALUES
('2017-01-02', 2),
('2017-01-03', 4),
('2017-01-04', 1),
('2017-01-05', 3),
('2017-01-06', 1),
('2017-01-07', 4),
('2017-01-08', 5),
('2017-01-09', -2),
('2017-01-10', 0),
('2017-01-11', -5),
('2017-01-12', 6),
('2017-01-13', 4),
('2017-01-14', 6)
;
WITH cte AS (SELECT DATE(`date_time`) AS `date`,
                    `data`,
                    MAX(`data`) OVER (ORDER BY `date_time`) AS `data_max`
             FROM `test`),
cte2 AS (SELECT `date`,
                `data`,
                `data_max`,
                CASE WHEN `data` < `data_max` THEN `data` - `data_max` END AS `data_diff`
         FROM cte),
cte3 AS (SELECT `date`, 
                MIN(`data_diff`) OVER (PARTITION BY `data_max` ORDER BY `date`) AS `diff_max`
         FROM cte2),
cte4 AS (SELECT `date`, `diff_max`, LAG(`diff_max`) OVER (ORDER BY `date`) AS `old_diff_max`
         FROM cte3)
SELECT `date`, `diff_max`
FROM cte4
WHERE `diff_max` < `old_diff_max` OR `old_diff_max` IS NULL AND `diff_max` IS NOT NULL


date
diff_max


2017-01-04
-3

2017-01-09
-7

2017-01-11
-10

2017-01-13
-2


WITH cte AS (SELECT DATE(`date_time`) AS `date`,
                    `data`,
                    MAX(`data`) OVER (ORDER BY `date_time`) AS `data_max`
             FROM `test`),
cte2 AS (SELECT `date`,
                `data`,
                `data_max`,
                CASE WHEN `data` < `data_max` THEN `data` - `data_max` END AS `data_diff`
         FROM cte),
cte3 AS (SELECT `data_max`, `date`, 
                MIN(`data_diff`) OVER (PARTITION BY `data_max` ORDER BY date) AS `diff_max`
         FROM cte2),
cte4 AS (SELECT `data_max`, `date`, `diff_max`, 
                LAG(`diff_max`) OVER (ORDER BY `date`) AS `old_diff_max`
         FROM cte3),
cte5 AS (SELECT `date`, `diff_max`, 
                RANK() OVER (PARTITION BY `data_max` ORDER BY `diff_max`) AS `diff_rank`
         FROM cte4
         WHERE `diff_max` < `old_diff_max` OR `old_diff_max` IS NULL AND `diff_max` IS NOT NULL),
cte6 AS (SELECT `data_max`, 
                MIN(CASE WHEN `data_diff` IS NOT NULL THEN date END) AS diff_date_from,
                MAX(CASE WHEN `data_diff` IS NOT NULL THEN date END) AS diff_date_to
         FROM cte2
         GROUP BY `data_max`
         HAVING diff_date_from IS NOT NULL)
SELECT diff_date_from, diff_date_to, `date` AS diff_max_date, `diff_max`
FROM cte6
JOIN cte5 ON cte5.date BETWEEN cte6.diff_date_from AND cte6.diff_date_to
WHERE cte5.diff_rank = 1


diff_date_from
diff_date_to
diff_max_date
diff_max


2017-01-04
2017-01-06
2017-01-04
-3

2017-01-09
2017-01-11
2017-01-11
-10

2017-01-13
2017-01-13
2017-01-13
-2
diff_date_from	diff_date_to	diff_max_date	diff_max
2017-01-04	2017-01-06	2017-01-04	-3
2017-01-09	2017-01-11	2017-01-11	-10
2017-01-13	2017-01-13	2017-01-13	-2