将统计聚合应用于时间序列数据

PostgreSQL 中的时间序列分析

Jasmin Ludolf

Content Developer, DataCamp

统计聚合

聚合函数：MIN(), MAX(), SUM(), AVG(), COUNT()
统计聚合：均值与中位数

插图：四个人围在展示分析和统计可视化的看板前。

计算平均值

SELECT
  AVG(views)::INTEGER as avg_views
  title
FROM dc_news_fact
JOIN dc_news_dim USING(id)
GROUP BY title
ORDER BY avg_views DESC;

|avg_views|title                      |
|---------|---------------------------|
|      207|For the Wealthiest, a Pr...|
|       12|Pet surrenders on rise a...|
|       12|Argentina's New Presiden...|
|        7|These 5 charts prove tha...|
|        7|How Is the Economy Doing...|

每日平均浏览量

WITH day_views AS (
  SELECT id, ts::DATE AS date, SUM(views) AS views
  FROM dc_news_fact
  GROUP BY id, date
)
SELECT
  AVG(views)::INTEGER AS avg
  title
FROM day_views JOIN dc_news_dim USING(id)
GROUP BY title
ORDER BY avg DESC;

每日平均浏览量

| avg|title                                                            |
|----|-----------------------------------------------------------------|
|9855|For the Wealthiest, a Private Tax System That Saves Them Billions|
| 579|Pet surrenders on rise as Fort McMurray's economy falls          |
| 574|Argentina's New President Moves Swiftly to Shake Up the Economy  |
| 352|How Is the Economy Doing? Politics May Decide Your Answer        |
| 348|These 5 charts prove that the economy does better under ...      |

每日平均浏览量

SELECT
  (SUM(views)/COUNT(DISTINCT ts::DATE))::INTEGER as avg,
  title
FROM dc_news_fact JOIN dc_news_dim USING(id)
GROUP BY title 
ORDER BY avg DESC;

|avg |title                                                            |
|----|-----------------------------------------------------------------|
|9855|For the Wealthiest, a Private Tax System That Saves Them Billions|
| 579|Pet surrenders on rise as Fort McMurray's economy falls          |
| 574|Argentina's New President Moves Swiftly to Shake Up the Economy  |
...

离散与连续中位数

离散中位数：最接近中间值的第一个值
连续中位数：将数据集一分为二的值

元素个数为奇数

序列 = (1, 2, 3, 4, 5)
离散中位数 = 3
连续中位数 = 3

元素个数为偶数

序列 = (1, 2, 3, 4)
离散中位数 = 2
连续中位数 = 2.5

有序集合聚合函数

PERCENTILE_DISC()
PERCENTILE_CONT()
有序集合聚合函数：PERCENTILE_DISC(fraction) WITHIN GROUP (ORDER BY field)

SELECT
  PERCENTILE_CONT(0.5) WITHIN GROUP
  (ORDER BY value) AS median_cont,
  PERCENTILE_DISC(0.5) WITHIN GROUP
  (ORDER BY value) AS median_disc
FROM
(
  VALUES
  (1,1), (1,2), (1,3), (1,4), (1,5),
  (2,1), (2,5), (2,7), (2,11), (2,11)
) AS t (id, value)
GROUP BY id;

有序集合聚合函数

|median_cont|median_disc|
|-----------|-----------|
|        3.0|          3|
|        7.0|          7|

中位数、分位数、百分位数、四分位数

中位数是一种百分位数
百分位数是一种分位数

分位数：将样本划分为近乎相等的子集
- 四分位（四个子集）
- 十分位（十个子集）

计算四分位数

SELECT
  PERCENTILE_DISC(0.25) WITHIN GROUP (ORDER BY value) AS ptile_25,
  PERCENTILE_DISC(0.5) WITHIN GROUP (ORDER BY value) AS ptile_50,
  PERCENTILE_DISC(0.75) WITHIN GROUP (ORDER BY value) AS ptile_75
FROM
(
  VALUES 
  (1,1), (1,2), (1,3), (1,4), (1,5)
) AS t (id, value)
GROUP BY id;

|ptile_25|ptile_50|ptile_75|
|--------|--------|--------|
|       2|       3|       4|

计算离散四分位数组

SELECT
  PERCENTILE_DISC(ARRAY[0.25, 0.5, 0.75]) 
  WITHIN GROUP (ORDER BY value) AS median_disc
FROM (
  VALUES
  (1,1), (1,2), (1,3), (1,4), (1,5) )
  AS t (id, value)
GROUP BY id;

|median_disc|
|-----------|
|{2,3,4}    |

让我们来练习！

PostgreSQL 中的时间序列分析