使用SQL查找时间序列值的最大值和最小值

Question

我有一组指数值随着时间的推移而增加和减少。我希望确定价值上升和价值下降的时间段。数据如下所示：

我尝试按范围划分值，我绝对不认为我做得对。这是我写的查询，充其量只是给我订购日期

SELECT
  date,
  MAX(index) OVER (PARTITION BY MAX(CAST(index AS numeric))
  ORDER BY
    date)
FROM (
  SELECT
    (value1 - value2) AS index,
    date
  FROM
    `project.dataset.table` )
GROUP BY
  date,
  index
ORDER BY
  date

我的最终目的是，当我被要求获得最小值时，我想要实现一个类似于此类的查询，同样也适用于最大值

Row |    date    |       minimas
-------------------------------------
1   | 2017-02-04 | 0.3149100257069409
2   | 2017-12-05 | 0.5784622847441183

Answer 1

处理相邻的重复值很棘手。您没有指定希望如何处理这些内容。如果您只想要第一个这样的值，那么过滤工作：

对于当地最小值：

SELECT Row, date, f0 AS minimal
FROM (SELECT t.*,
             LEAD(f0) OVER (ORDER BY DATE) as f0_lead
      FROM (SELECT t.*,
                   LAG(f0) OVER (ORDER BY date) AS f0_lag
            FROM `project.dataset.table` t
           ) t
      WHERE f0_lag IS NULL or f0_lag <> f0
     ) t
WHERE (f0 < f0_lag or f0_lag is null) and
      (f0 < f0_lead or f0_lead is null);

或者，如果您愿意，可以简化比较：

SELECT Row, date, f0 AS minimal
FROM (SELECT t.*,
             LEAD(f0) OVER (ORDER BY DATE) as f0_lead
      FROM (SELECT t.*,
                   LAG(f0) OVER (ORDER BY date) AS f0_lag
            FROM t
           ) t
      WHERE f0_lag IS NULL or f0 < f0_lag
     ) t
WHERE f0 < f0_lead or f0_lead is null;

当<s改为>s时，局部最大值可以遵循相同的逻辑。

Here是一个db <>小提琴（使用Postgres，但这没关系）。

编辑：

连续返回所有最小值/最大值更具挑战性。以下适用于BigQuery：

WITH t AS (
    SELECT 1 AS Row, '2017-01-19' AS date, 0.3904 AS f0 UNION ALL
    SELECT 2,  '2017-02-04', 0.3149 UNION ALL
    SELECT 2.5,  '2017-02-05', 0.3149 UNION ALL
    SELECT 3,  '2017-03-24', 0.3302 UNION ALL
    SELECT 4,  '2017-04-09', 0.5339 UNION ALL
    SELECT 5,  '2017-05-11', 0.7753 UNION ALL
    SELECT 6,  '2017-05-27', 0.8539 UNION ALL
    SELECT 7,  '2017-09-16', 0.8803 UNION ALL
    SELECT 7.5,  '2017-09-17', 0.8803 UNION ALL
    SELECT 7.7,  '2017-09-18', 0.8803 UNION ALL
    SELECT 8,  '2017-10-02', 0.8570 UNION ALL
    SELECT 9,  '2017-11-03', 0.7744 UNION ALL
    SELECT 10, '2017-11-19', 0.6092 UNION ALL
    SELECT 11, '2017-12-05', 0.5785
)
SELECT t.*
FROM (SELECT t.*,
             MAX(f0_lag) OVER (PARTITION BY grp) as grp_f0_lag,
             MAX(f0_lead) OVER (PARTITION BY grp) as grp_f0_lead
      FROM (SELECT t.*,
                   COUNTIF(f0_lag <> f0) OVER (ORDER BY DATE) as grp,
                   LEAD(f0) OVER (ORDER BY DATE) as f0_lead
            FROM (SELECT t.*,
                         LAG(f0) OVER (ORDER BY date) AS f0_lag
                  FROM t
                 ) t
           ) t
     ) t
WHERE (f0 < grp_f0_lag or grp_f0_lag is null) and
      (f0 < grp_f0_lead or grp_f0_lead is null) ;

基本上，这是识别相邻值的组。然后它通过组传播最大lag()和lead()值（最大值，你想传播最小值）。

然后将整个组视为一个单元并在结果集中处理。

Answer 2

以下是BigQuery Standard SQL

#standardSQL
SELECT * EXCEPT(prev, next), 
  CASE 
    WHEN prev < next THEN 'min'
    WHEN prev > next THEN 'max'
    WHEN prev IS NULL THEN 'start'
    WHEN next IS NULL THEN 'finish'
  END extremum
FROM (
  SELECT *, 
    SIGN(index - LAG(index) OVER(ORDER BY DAY)) prev, 
    SIGN(LEAD(index) OVER(ORDER BY DAY) - index) next
  FROM `project.dataset.table`
)
WHERE IFNULL(prev != next, TRUE)

您可以使用问题中的示例数据进行测试，使用上面的示例，如下例所示

#standardSQL
WITH `project.dataset.table` AS (
  SELECT DATE '2017-01-19' day, 0.39 index UNION ALL
  SELECT '2017-02-04', 0.31 UNION ALL
  SELECT '2017-03-24', 0.33 UNION ALL
  SELECT '2017-04-09', 0.53 UNION ALL
  SELECT '2017-05-11', 0.77 UNION ALL
  SELECT '2017-05-27', 0.85 UNION ALL
  SELECT '2017-09-16', 0.88 UNION ALL
  SELECT '2017-10-02', 0.85 UNION ALL
  SELECT '2017-11-03', 0.77 UNION ALL
  SELECT '2017-11-19', 0.61 UNION ALL
  SELECT '2017-12-05', 0.57 
)
SELECT * EXCEPT(prev, next), 
  CASE 
    WHEN prev < next THEN 'min'
    WHEN prev > next THEN 'max'
    WHEN prev IS NULL THEN 'start'
    WHEN next IS NULL THEN 'finish'
  END extremum
FROM (
  SELECT *, 
    SIGN(index - LAG(index) OVER(ORDER BY DAY)) prev, 
    SIGN(LEAD(index) OVER(ORDER BY DAY) - index) next
  FROM `project.dataset.table`
)
WHERE IFNULL(prev != next, TRUE)
-- ORDER BY day

结果

Row day         index   extremum     
1   2017-01-19  0.39    start    
2   2017-02-04  0.31    min  
3   2017-09-16  0.88    max  
4   2017-12-05  0.57    finish    

Answer 3

我们可以将局部最小值定义为x轴上的时间点，其中前后的响应值都大于最小点的值。如果两端都有端点，则只需要一个值。我们可以尝试在这里使用LEAD和LAG函数：

SELECT Row, date, f0 AS minimal
FROM
(
    SELECT Row, date, f0,
        LAG(f0, 1, f0 + 0.1) OVER (ORDER BY date) AS f0_lag,
        LEAD(f0, 1, f0 + 0.1) OVER (ORDER BY date) AS f0_lead
    FROM project.dataset.table
) t
WHERE f0 < f0_lag AND f0 < f0_lead;

这是使用您的样本数据的demo in SQL Server。由于我的答案是基于SQL Server，因为我无法访问BigQuery，您可能需要稍微调整我使用的语法。