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Periodos de tiempo de consulta de MySQL y valor de caída máxima frente al valor máximo anterior

Sospecho que pueden optimizarse un poco, pero estas consultas deberían brindarle los resultados que desea. Comparten los mismos primeros 3 CTE que generan el diff_max valor para cada data_max . En la primera consulta buscamos un cambio en ese valor (de NULL a un valor, o una disminución en el valor) para generar las filas de salida. Los CTE 4 y 5 de la segunda consulta son similares a la primera consulta, pero agregamos un RANK al diff_max valores, para que podamos JOIN el valor mínimo (con su fecha asociada) al date_diff_from y date_diff_to valores del sexto CTE (que es lo mismo que mi respuesta a su otra pregunta ).

Pregunta 1:

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

Salida:

date        diff_max
2017-01-04  -3
2017-01-09  -7
2017-01-11  -10
2017-01-13  -2

Pregunta 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

Salida:

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

Demostración en dbfiddle