Work with time series data

This document describes how to use SQL functions to support time series analysis.

Introduction

A time series is a sequence of data points, each consisting of a time and a value associated with that time. Usually, a time series also has an identifier, which uniquely names the time series.

In relational databases, a time series is modeled as a table with the following groups of columns:

Time column
Might have partitioning columns, for example, zip code
One or more value columns, or a STRUCT type combining multiple values, for example, temperature and AQI

The following is an example of time series data modeled as a table:

Time series table example.

Aggregate a time series

In time series analysis, time aggregation is an aggregation performed along the time axis.

You can perform time aggregation in BigQuery with the help of time bucketing functions (TIMESTAMP_BUCKET, DATE_BUCKET, and DATETIME_BUCKET). Time bucketing functions map input time values to the bucket they belong to.

Typically, time aggregation is performed to combine multiple data points in a time window into a single data point, using an aggregation function, such as AVG, MIN, MAX, COUNT, or SUM. For example, 15-minute average request latency, daily minimum and maximum temperatures, and daily number of taxi trips.

For the queries in this section, create a table called mydataset.environmental_data_hourly:

CREATE OR REPLACE TABLE mydataset.environmental_data_hourly AS
SELECT * FROM UNNEST(
  ARRAY<STRUCT<zip_code INT64, time TIMESTAMP, aqi INT64, temperature INT64>>[
    STRUCT(60606, TIMESTAMP '2020-09-08 00:30:51', 22, 66),
    STRUCT(60606, TIMESTAMP '2020-09-08 01:32:10', 23, 63),
    STRUCT(60606, TIMESTAMP '2020-09-08 02:30:35', 22, 60),
    STRUCT(60606, TIMESTAMP '2020-09-08 03:29:39', 21, 58),
    STRUCT(60606, TIMESTAMP '2020-09-08 04:33:05', 21, 59),
    STRUCT(60606, TIMESTAMP '2020-09-08 05:32:01', 21, 57),
    STRUCT(60606, TIMESTAMP '2020-09-08 06:31:14', 22, 56),
    STRUCT(60606, TIMESTAMP '2020-09-08 07:31:06', 28, 55),
    STRUCT(60606, TIMESTAMP '2020-09-08 08:29:59', 30, 55),
    STRUCT(60606, TIMESTAMP '2020-09-08 09:29:34', 31, 55),
    STRUCT(60606, TIMESTAMP '2020-09-08 10:31:24', 38, 56),
    STRUCT(60606, TIMESTAMP '2020-09-08 11:31:24', 38, 56),
    STRUCT(60606, TIMESTAMP '2020-09-08 12:32:38', 38, 57),
    STRUCT(60606, TIMESTAMP '2020-09-08 13:29:59', 38, 56),
    STRUCT(60606, TIMESTAMP '2020-09-08 14:31:22', 43, 59),
    STRUCT(60606, TIMESTAMP '2020-09-08 15:31:38', 42, 63),
    STRUCT(60606, TIMESTAMP '2020-09-08 16:34:22', 43, 65),
    STRUCT(60606, TIMESTAMP '2020-09-08 17:33:23', 42, 68),
    STRUCT(60606, TIMESTAMP '2020-09-08 18:28:47', 36, 69),
    STRUCT(60606, TIMESTAMP '2020-09-08 19:30:28', 34, 67),
    STRUCT(60606, TIMESTAMP '2020-09-08 20:30:53', 29, 67),
    STRUCT(60606, TIMESTAMP '2020-09-08 21:32:28', 27, 67),
    STRUCT(60606, TIMESTAMP '2020-09-08 22:31:45', 25, 65),
    STRUCT(60606, TIMESTAMP '2020-09-08 23:31:02', 22, 63),
    STRUCT(94105, TIMESTAMP '2020-09-08 00:07:11', 60, 74),
    STRUCT(94105, TIMESTAMP '2020-09-08 01:07:24', 61, 73),
    STRUCT(94105, TIMESTAMP '2020-09-08 02:08:07', 60, 71),
    STRUCT(94105, TIMESTAMP '2020-09-08 03:11:05', 69, 69),
    STRUCT(94105, TIMESTAMP '2020-09-08 04:07:26', 72, 67),
    STRUCT(94105, TIMESTAMP '2020-09-08 05:08:11', 70, 66),
    STRUCT(94105, TIMESTAMP '2020-09-08 06:07:30', 68, 65),
    STRUCT(94105, TIMESTAMP '2020-09-08 07:07:10', 77, 64),
    STRUCT(94105, TIMESTAMP '2020-09-08 08:06:35', 81, 64),
    STRUCT(94105, TIMESTAMP '2020-09-08 09:10:18', 82, 63),
    STRUCT(94105, TIMESTAMP '2020-09-08 10:08:10', 107, 62),
    STRUCT(94105, TIMESTAMP '2020-09-08 11:08:01', 115, 62),
    STRUCT(94105, TIMESTAMP '2020-09-08 12:07:39', 120, 62),
    STRUCT(94105, TIMESTAMP '2020-09-08 13:06:03', 125, 61),
    STRUCT(94105, TIMESTAMP '2020-09-08 14:08:37', 129, 62),
    STRUCT(94105, TIMESTAMP '2020-09-08 15:09:19', 150, 62),
    STRUCT(94105, TIMESTAMP '2020-09-08 16:06:39', 151, 62),
    STRUCT(94105, TIMESTAMP '2020-09-08 17:08:01', 155, 63),
    STRUCT(94105, TIMESTAMP '2020-09-08 18:09:23', 154, 64),
    STRUCT(94105, TIMESTAMP '2020-09-08 19:08:43', 151, 67),
    STRUCT(94105, TIMESTAMP '2020-09-08 20:07:19', 150, 69),
    STRUCT(94105, TIMESTAMP '2020-09-08 21:07:37', 148, 72),
    STRUCT(94105, TIMESTAMP '2020-09-08 22:08:01', 143, 76),
    STRUCT(94105, TIMESTAMP '2020-09-08 23:08:41', 137, 75)
]);

/*---------------------+----------+-----------------+-----------------+
 |        time         | zip_code | temperature_min | temperature_max |
 +---------------------+----------+-----------------+-----------------+
 | 2020-09-08 00:00:00 |    60606 |              60 |              66 |
 | 2020-09-08 03:00:00 |    60606 |              57 |              59 |
 | 2020-09-08 06:00:00 |    60606 |              55 |              56 |
 | 2020-09-08 09:00:00 |    60606 |              55 |              56 |
 | 2020-09-08 12:00:00 |    60606 |              56 |              59 |
 | 2020-09-08 15:00:00 |    60606 |              63 |              68 |
 | 2020-09-08 18:00:00 |    60606 |              67 |              69 |
 | 2020-09-08 21:00:00 |    60606 |              63 |              67 |
 | 2020-09-08 00:00:00 |    94105 |              71 |              74 |
 | 2020-09-08 03:00:00 |    94105 |              66 |              69 |
 | 2020-09-08 06:00:00 |    94105 |              64 |              65 |
 | 2020-09-08 09:00:00 |    94105 |              62 |              63 |
 | 2020-09-08 12:00:00 |    94105 |              61 |              62 |
 | 2020-09-08 15:00:00 |    94105 |              62 |              63 |
 | 2020-09-08 18:00:00 |    94105 |              64 |              69 |
 | 2020-09-08 21:00:00 |    94105 |              72 |              76 |
 +---------------------+----------+-----------------+-----------------*/

One interesting observation about the preceding data is that measurements are taken at arbitrary time periods, known as unaligned time series. Aggregation is one of the ways by which a time series can be aligned.

Get a 3-hour average

The following query computes a 3-hour average air quality index (AQI) and temperature for each zip code. The TIMESTAMP_BUCKET function performs time aggregation by assigning each time value to a particular day.

SELECT
  TIMESTAMP_BUCKET(time, INTERVAL 3 HOUR) AS time,
  zip_code,
  CAST(AVG(aqi) AS INT64) AS aqi,
  CAST(AVG(temperature) AS INT64) AS temperature
FROM mydataset.environmental_data_hourly
GROUP BY zip_code, time
ORDER BY zip_code, time;

/*---------------------+----------+-----+-------------+
 |        time         | zip_code | aqi | temperature |
 +---------------------+----------+-----+-------------+
 | 2020-09-08 00:00:00 |    60606 |  22 |          63 |
 | 2020-09-08 03:00:00 |    60606 |  21 |          58 |
 | 2020-09-08 06:00:00 |    60606 |  27 |          55 |
 | 2020-09-08 09:00:00 |    60606 |  36 |          56 |
 | 2020-09-08 12:00:00 |    60606 |  40 |          57 |
 | 2020-09-08 15:00:00 |    60606 |  42 |          65 |
 | 2020-09-08 18:00:00 |    60606 |  33 |          68 |
 | 2020-09-08 21:00:00 |    60606 |  25 |          65 |
 | 2020-09-08 00:00:00 |    94105 |  60 |          73 |
 | 2020-09-08 03:00:00 |    94105 |  70 |          67 |
 | 2020-09-08 06:00:00 |    94105 |  75 |          64 |
 | 2020-09-08 09:00:00 |    94105 | 101 |          62 |
 | 2020-09-08 12:00:00 |    94105 | 125 |          62 |
 | 2020-09-08 15:00:00 |    94105 | 152 |          62 |
 | 2020-09-08 18:00:00 |    94105 | 152 |          67 |
 | 2020-09-08 21:00:00 |    94105 | 143 |          74 |
 +---------------------+----------+-----+-------------*/

Get a 3-hour minimum and maximum value

In the following query, you compute 3-hour minimum and maximum temperatures for each zip code:

SELECT
  TIMESTAMP_BUCKET(time, INTERVAL 3 HOUR) AS time,
  zip_code,
  MIN(temperature) AS temperature_min,
  MAX(temperature) AS temperature_max,
FROM mydataset.environmental_data_hourly
GROUP BY zip_code, time
ORDER BY zip_code, time;

/*---------------------+----------+-----------------+-----------------+
 |        time         | zip_code | temperature_min | temperature_max |
 +---------------------+----------+-----------------+-----------------+
 | 2020-09-08 00:00:00 |    60606 |              60 |              66 |
 | 2020-09-08 03:00:00 |    60606 |              57 |              59 |
 | 2020-09-08 06:00:00 |    60606 |              55 |              56 |
 | 2020-09-08 09:00:00 |    60606 |              55 |              56 |
 | 2020-09-08 12:00:00 |    60606 |              56 |              59 |
 | 2020-09-08 15:00:00 |    60606 |              63 |              68 |
 | 2020-09-08 18:00:00 |    60606 |              67 |              69 |
 | 2020-09-08 21:00:00 |    60606 |              63 |              67 |
 | 2020-09-08 00:00:00 |    94105 |              71 |              74 |
 | 2020-09-08 03:00:00 |    94105 |              66 |              69 |
 | 2020-09-08 06:00:00 |    94105 |              64 |              65 |
 | 2020-09-08 09:00:00 |    94105 |              62 |              63 |
 | 2020-09-08 12:00:00 |    94105 |              61 |              62 |
 | 2020-09-08 15:00:00 |    94105 |              62 |              63 |
 | 2020-09-08 18:00:00 |    94105 |              64 |              69 |
 | 2020-09-08 21:00:00 |    94105 |              72 |              76 |
 +---------------------+----------+-----------------+-----------------*/

Get a 3-hour average with custom alignment

When you perform time series aggregation, you use a specific alignment for time series windows, either implicitly or explicitly. The preceding queries used implicit alignment, which produced buckets that started at times like 00:00:00, 03:00:00, and 06:00:00. To explicitly set this alignment in the TIMESTAMP_BUCKET function, pass an optional argument that specifies the origin.

In the following query, the origin is set as 2020-01-01 02:00:00. This changes the alignment and produces buckets that start at times like 02:00:00, 05:00:00, and 08:00:00:

SELECT
  TIMESTAMP_BUCKET(time, INTERVAL 3 HOUR, TIMESTAMP '2020-01-01 02:00:00') AS time,
  zip_code,
  CAST(AVG(aqi) AS INT64) AS aqi,
  CAST(AVG(temperature) AS INT64) AS temperature
FROM mydataset.environmental_data_hourly
GROUP BY zip_code, time
ORDER BY zip_code, time;

/*---------------------+----------+-----+-------------+
 |        time         | zip_code | aqi | temperature |
 +---------------------+----------+-----+-------------+
 | 2020-09-07 23:00:00 |    60606 |  23 |          65 |
 | 2020-09-08 02:00:00 |    60606 |  21 |          59 |
 | 2020-09-08 05:00:00 |    60606 |  24 |          56 |
 | 2020-09-08 08:00:00 |    60606 |  33 |          55 |
 | 2020-09-08 11:00:00 |    60606 |  38 |          56 |
 | 2020-09-08 14:00:00 |    60606 |  43 |          62 |
 | 2020-09-08 17:00:00 |    60606 |  37 |          68 |
 | 2020-09-08 20:00:00 |    60606 |  27 |          66 |
 | 2020-09-08 23:00:00 |    60606 |  22 |          63 |
 | 2020-09-07 23:00:00 |    94105 |  61 |          74 |
 | 2020-09-08 02:00:00 |    94105 |  67 |          69 |
 | 2020-09-08 05:00:00 |    94105 |  72 |          65 |
 | 2020-09-08 08:00:00 |    94105 |  90 |          63 |
 | 2020-09-08 11:00:00 |    94105 | 120 |          62 |
 | 2020-09-08 14:00:00 |    94105 | 143 |          62 |
 | 2020-09-08 17:00:00 |    94105 | 153 |          65 |
 | 2020-09-08 20:00:00 |    94105 | 147 |          72 |
 | 2020-09-08 23:00:00 |    94105 | 137 |          75 |
 +---------------------+----------+-----+-------------*/

Aggregate a time series with gap filling

Sometimes after you aggregate a time series, the data might have gaps that need to be filled with some values for further analysis or presentation of the data. The technique used to fill in those gaps is called gap filling. In BigQuery, you can use the GAP_FILL table function for filling gaps in time series data, using one of the provided gap-filling methods:

NULL, also known as constant
LOCF, last observation carried forward
Linear, linear interpolation between the two neighboring data points

For the queries in this section, create a table called mydataset.environmental_data_hourly_with_gaps, which is based on the data used in the preceding section, but with gaps in it. In the real world scenarios, data could have missing data points due to a short-term weather station malfunction.

CREATE OR REPLACE TABLE mydataset.environmental_data_hourly_with_gaps AS
SELECT * FROM UNNEST(
  ARRAY<STRUCT<zip_code INT64, time TIMESTAMP, aqi INT64, temperature INT64>>[
    STRUCT(60606, TIMESTAMP '2020-09-08 00:30:51', 22, 66),
    STRUCT(60606, TIMESTAMP '2020-09-08 01:32:10', 23, 63),
    STRUCT(60606, TIMESTAMP '2020-09-08 02:30:35', 22, 60),
    STRUCT(60606, TIMESTAMP '2020-09-08 03:29:39', 21, 58),
    STRUCT(60606, TIMESTAMP '2020-09-08 04:33:05', 21, 59),
    STRUCT(60606, TIMESTAMP '2020-09-08 05:32:01', 21, 57),
    STRUCT(60606, TIMESTAMP '2020-09-08 06:31:14', 22, 56),
    STRUCT(60606, TIMESTAMP '2020-09-08 07:31:06', 28, 55),
    STRUCT(60606, TIMESTAMP '2020-09-08 08:29:59', 30, 55),
    STRUCT(60606, TIMESTAMP '2020-09-08 09:29:34', 31, 55),
    STRUCT(60606, TIMESTAMP '2020-09-08 10:31:24', 38, 56),
    STRUCT(60606, TIMESTAMP '2020-09-08 11:31:24', 38, 56),
    -- No data points between hours 12 and 15.
    STRUCT(60606, TIMESTAMP '2020-09-08 16:34:22', 43, 65),
    STRUCT(60606, TIMESTAMP '2020-09-08 17:33:23', 42, 68),
    STRUCT(60606, TIMESTAMP '2020-09-08 18:28:47', 36, 69),
    STRUCT(60606, TIMESTAMP '2020-09-08 19:30:28', 34, 67),
    STRUCT(60606, TIMESTAMP '2020-09-08 20:30:53', 29, 67),
    STRUCT(60606, TIMESTAMP '2020-09-08 21:32:28', 27, 67),
    STRUCT(60606, TIMESTAMP '2020-09-08 22:31:45', 25, 65),
    STRUCT(60606, TIMESTAMP '2020-09-08 23:31:02', 22, 63),
    STRUCT(94105, TIMESTAMP '2020-09-08 00:07:11', 60, 74),
    STRUCT(94105, TIMESTAMP '2020-09-08 01:07:24', 61, 73),
    STRUCT(94105, TIMESTAMP '2020-09-08 02:08:07', 60, 71),
    STRUCT(94105, TIMESTAMP '2020-09-08 03:11:05', 69, 69),
    STRUCT(94105, TIMESTAMP '2020-09-08 04:07:26', 72, 67),
    STRUCT(94105, TIMESTAMP '2020-09-08 05:08:11', 70, 66),
    STRUCT(94105, TIMESTAMP '2020-09-08 06:07:30', 68, 65),
    STRUCT(94105, TIMESTAMP '2020-09-08 07:07:10', 77, 64),
    STRUCT(94105, TIMESTAMP '2020-09-08 08:06:35', 81, 64),
    STRUCT(94105, TIMESTAMP '2020-09-08 09:10:18', 82, 63),
    STRUCT(94105, TIMESTAMP '2020-09-08 10:08:10', 107, 62),
    STRUCT(94105, TIMESTAMP '2020-09-08 11:08:01', 115, 62),
    STRUCT(94105, TIMESTAMP '2020-09-08 12:07:39', 120, 62),
    STRUCT(94105, TIMESTAMP '2020-09-08 13:06:03', 125, 61),
    STRUCT(94105, TIMESTAMP '2020-09-08 14:08:37', 129, 62),
    -- No data points between hours 15 and 18.
    STRUCT(94105, TIMESTAMP '2020-09-08 19:08:43', 151, 67),
    STRUCT(94105, TIMESTAMP '2020-09-08 20:07:19', 150, 69),
    STRUCT(94105, TIMESTAMP '2020-09-08 21:07:37', 148, 72),
    STRUCT(94105, TIMESTAMP '2020-09-08 22:08:01', 143, 76),
    STRUCT(94105, TIMESTAMP '2020-09-08 23:08:41', 137, 75)
]);

Get a 3-hour average (include gaps)

The following query computes 3-hour average AQI and temperature for each zip code:

SELECT
  TIMESTAMP_BUCKET(time, INTERVAL 3 HOUR) AS time,
  zip_code,
  CAST(AVG(aqi) AS INT64) AS aqi,
  CAST(AVG(temperature) AS INT64) AS temperature
FROM mydataset.environmental_data_hourly_with_gaps
GROUP BY zip_code, time
ORDER BY zip_code, time;

/*---------------------+----------+-----+-------------+
 |        time         | zip_code | aqi | temperature |
 +---------------------+----------+-----+-------------+
 | 2020-09-08 00:00:00 |    60606 |  22 |          63 |
 | 2020-09-08 03:00:00 |    60606 |  21 |          58 |
 | 2020-09-08 06:00:00 |    60606 |  27 |          55 |
 | 2020-09-08 09:00:00 |    60606 |  36 |          56 |
 | 2020-09-08 15:00:00 |    60606 |  43 |          67 |
 | 2020-09-08 18:00:00 |    60606 |  33 |          68 |
 | 2020-09-08 21:00:00 |    60606 |  25 |          65 |
 | 2020-09-08 00:00:00 |    94105 |  60 |          73 |
 | 2020-09-08 03:00:00 |    94105 |  70 |          67 |
 | 2020-09-08 06:00:00 |    94105 |  75 |          64 |
 | 2020-09-08 09:00:00 |    94105 | 101 |          62 |
 | 2020-09-08 12:00:00 |    94105 | 125 |          62 |
 | 2020-09-08 18:00:00 |    94105 | 151 |          68 |
 | 2020-09-08 21:00:00 |    94105 | 143 |          74 |
 +---------------------+----------+-----+-------------*/

Note how the output has gaps at certain time intervals. For example, the time series for zip code 60606 doesn't have a data point at 2020-09-08 12:00:00, and the time series for zip code 94105 doesn't have a data point at 2020-09-08 15:00:00.

Get a 3-hour average (fill gaps)

Use the query from the previous section and add the GAP_FILL function to fill the gaps:

WITH aggregated_3_hr AS (
  SELECT
    TIMESTAMP_BUCKET(time, INTERVAL 3 HOUR) AS time,
    zip_code,
    CAST(AVG(aqi) AS INT64) AS aqi,
    CAST(AVG(temperature) AS INT64) AS temperature
   FROM mydataset.environmental_data_hourly_with_gaps
   GROUP BY zip_code, time)

SELECT *
FROM GAP_FILL(
  TABLE aggregated_3_hr,
  ts_column => 'time',
  bucket_width => INTERVAL 3 HOUR,
  partitioning_columns => ['zip_code']
)
ORDER BY zip_code, time;

/*---------------------+----------+------+-------------+
 |        time         | zip_code | aqi  | temperature |
 +---------------------+----------+------+-------------+
 | 2020-09-08 00:00:00 |    60606 |   22 |          63 |
 | 2020-09-08 03:00:00 |    60606 |   21 |          58 |
 | 2020-09-08 06:00:00 |    60606 |   27 |          55 |
 | 2020-09-08 09:00:00 |    60606 |   36 |          56 |
 | 2020-09-08 12:00:00 |    60606 | NULL |        NULL |
 | 2020-09-08 15:00:00 |    60606 |   43 |          67 |
 | 2020-09-08 18:00:00 |    60606 |   33 |          68 |
 | 2020-09-08 21:00:00 |    60606 |   25 |          65 |
 | 2020-09-08 00:00:00 |    94105 |   60 |          73 |
 | 2020-09-08 03:00:00 |    94105 |   70 |          67 |
 | 2020-09-08 06:00:00 |    94105 |   75 |          64 |
 | 2020-09-08 09:00:00 |    94105 |  101 |          62 |
 | 2020-09-08 12:00:00 |    94105 |  125 |          62 |
 | 2020-09-08 15:00:00 |    94105 | NULL |        NULL |
 | 2020-09-08 18:00:00 |    94105 |  151 |          68 |
 | 2020-09-08 21:00:00 |    94105 |  143 |          74 |
 +---------------------+----------+------+-------------*/

The output table now contains a missing row at 2020-09-08 12:00:00 for zip code 60606 and at 2020-09-08 15:00:00 for zip code 94105, with NULL values in the corresponding metric columns. Since you didn't specify any gap-filling method, GAP_FILL used the default gap-filling method, NULL.

Fill gaps with linear and LOCF gap filling

In the following query, the GAP_FILL function is used with the LOCF gap-filling method for the aqi column and linear interpolation for the temperature column:

WITH aggregated_3_hr AS (
  SELECT
    TIMESTAMP_BUCKET(time, INTERVAL 3 HOUR) AS time,
    zip_code,
    CAST(AVG(aqi) AS INT64) AS aqi,
    CAST(AVG(temperature) AS INT64) AS temperature
   FROM mydataset.environmental_data_hourly_with_gaps
   GROUP BY zip_code, time)

SELECT *
FROM GAP_FILL(
  TABLE aggregated_3_hr,
  ts_column => 'time',
  bucket_width => INTERVAL 3 HOUR,
  partitioning_columns => ['zip_code'],
  value_columns => [
    ('aqi', 'locf'),
    ('temperature', 'linear')
  ]
)
ORDER BY zip_code, time;

/*---------------------+----------+-----+-------------+
 |        time         | zip_code | aqi | temperature |
 +---------------------+----------+-----+-------------+
 | 2020-09-08 00:00:00 |    60606 |  22 |          63 |
 | 2020-09-08 03:00:00 |    60606 |  21 |          58 |
 | 2020-09-08 06:00:00 |    60606 |  27 |          55 |
 | 2020-09-08 09:00:00 |    60606 |  36 |          56 |
 | 2020-09-08 12:00:00 |    60606 |  36 |          62 |
 | 2020-09-08 15:00:00 |    60606 |  43 |          67 |
 | 2020-09-08 18:00:00 |    60606 |  33 |          68 |
 | 2020-09-08 21:00:00 |    60606 |  25 |          65 |
 | 2020-09-08 00:00:00 |    94105 |  60 |          73 |
 | 2020-09-08 03:00:00 |    94105 |  70 |          67 |
 | 2020-09-08 06:00:00 |    94105 |  75 |          64 |
 | 2020-09-08 09:00:00 |    94105 | 101 |          62 |
 | 2020-09-08 12:00:00 |    94105 | 125 |          62 |
 | 2020-09-08 15:00:00 |    94105 | 125 |          65 |
 | 2020-09-08 18:00:00 |    94105 | 151 |          68 |
 | 2020-09-08 21:00:00 |    94105 | 143 |          74 |
 +---------------------+----------+-----+-------------*/

In this query, the first gap-filled row has aqi value 36, which is taken from the previous data point of this time series (zip code 60606) at 2020-09-08 09:00:00. The temperature value 62 is a result of linear interpolation between data points 2020-09-08 09:00:00 and 2020-09-08 15:00:00. The other missing row was created in a similar way - aqi value 125 was carried over from the previous data point of this time series (zip code 94105), and the temperature value 65 is a result of linear interpolation between the previous and the next available data points.

Align a time series with gap filling

Time series can be aligned or unaligned. A time series is aligned when data points only occur at regular intervals.

In the real world, at the time of collection, time series are rarely aligned and usually require some further processing to align them.

For example, consider IoT devices that send their metrics to a centralized collector every minute. It would be unreasonable to expect the devices to send their metrics at exactly the same instants of time. Usually, each device sends its metrics with the same frequency (period) but with different time offset (alignment). The following diagram illustrates this example. You can see each device sending its data with a one-minute interval with some instances of missing data (Device 3 at 9:36:39 ) and delayed data (Device 1 at 9:37:28).

Align time series example

You can perform time series alignment on unaligned data, using time aggregation. This is helpful if you want to change the sampling period of the time series, such as changing from the original 1-minute sampling period to a 15-minute period. You can align data for further time series processing, such as joining the time series data, or for display purposes (such as graphing).

You can use the GAP_FILL table function with LOCF or linear gap-filling methods to perform time series alignment. The idea is to use GAP_FILL with the selected output period and alignment (controlled by the optional origin argument). The result of the operation is a table with aligned time series, where values for each data point are derived from the input time series with the gap-filling method used for that particular value column (LOCF of linear).

Create a table mydataset.device_data, which resembles the previous illustration:

CREATE OR REPLACE TABLE mydataset.device_data AS
SELECT * FROM UNNEST(
  ARRAY<STRUCT<device_id INT64, time TIMESTAMP, signal INT64, state STRING>>[
    STRUCT(2, TIMESTAMP '2023-11-01 09:35:07', 87, 'ACTIVE'),
    STRUCT(1, TIMESTAMP '2023-11-01 09:35:26', 82, 'ACTIVE'),
    STRUCT(3, TIMESTAMP '2023-11-01 09:35:39', 74, 'INACTIVE'),
    STRUCT(2, TIMESTAMP '2023-11-01 09:36:07', 88, 'ACTIVE'),
    STRUCT(1, TIMESTAMP '2023-11-01 09:36:26', 82, 'ACTIVE'),
    STRUCT(2, TIMESTAMP '2023-11-01 09:37:07', 88, 'ACTIVE'),
    STRUCT(1, TIMESTAMP '2023-11-01 09:37:28', 80, 'ACTIVE'),
    STRUCT(3, TIMESTAMP '2023-11-01 09:37:39', 77, 'ACTIVE'),
    STRUCT(2, TIMESTAMP '2023-11-01 09:38:07', 86, 'ACTIVE'),
    STRUCT(1, TIMESTAMP '2023-11-01 09:38:26', 81, 'ACTIVE'),
    STRUCT(3, TIMESTAMP '2023-11-01 09:38:39', 77, 'ACTIVE')
]);

The following is the actual data ordered by time and device_id columns:

SELECT * FROM mydataset.device_data ORDER BY time, device_id;

/*-----------+---------------------+--------+----------+
 | device_id |        time         | signal |  state   |
 +-----------+---------------------+--------+----------+
 |         2 | 2023-11-01 09:35:07 |     87 | ACTIVE   |
 |         1 | 2023-11-01 09:35:26 |     82 | ACTIVE   |
 |         3 | 2023-11-01 09:35:39 |     74 | INACTIVE |
 |         2 | 2023-11-01 09:36:07 |     88 | ACTIVE   |
 |         1 | 2023-11-01 09:36:26 |     82 | ACTIVE   |
 |         2 | 2023-11-01 09:37:07 |     88 | ACTIVE   |
 |         1 | 2023-11-01 09:37:28 |     80 | ACTIVE   |
 |         3 | 2023-11-01 09:37:39 |     77 | ACTIVE   |
 |         2 | 2023-11-01 09:38:07 |     86 | ACTIVE   |
 |         1 | 2023-11-01 09:38:26 |     81 | ACTIVE   |
 |         3 | 2023-11-01 09:38:39 |     77 | ACTIVE   |
 +-----------+---------------------+--------+----------*/

The table contains the time series for each device with two metric columns:

signal - signal level as observed by the device at the time of sampling, represented as an integer value between 0 and 100.
state - state of the device at the time of sampling, represented as a free form string.

In the following query, the GAP_FILL function is used to align the time series at 1-minute intervals. Note how linear interpolation is used to compute values for the signal column and LOCF for the state column. For this example data, linear interpolation is a suitable choice to compute the output values.

SELECT *
FROM GAP_FILL(
  TABLE mydataset.device_data,
  ts_column => 'time',
  bucket_width => INTERVAL 1 MINUTE,
  partitioning_columns => ['device_id'],
  value_columns => [
    ('signal', 'linear'),
    ('state', 'locf')
  ]
)
ORDER BY time, device_id;

 /*---------------------+-----------+--------+----------+
 |        time         | device_id | signal |  state   |
 +---------------------+-----------+--------+----------+
 | 2023-11-01 09:36:00 |         1 |     82 | ACTIVE   |
 | 2023-11-01 09:36:00 |         2 |     88 | ACTIVE   |
 | 2023-11-01 09:36:00 |         3 |     75 | INACTIVE |
 | 2023-11-01 09:37:00 |         1 |     81 | ACTIVE   |
 | 2023-11-01 09:37:00 |         2 |     88 | ACTIVE   |
 | 2023-11-01 09:37:00 |         3 |     76 | INACTIVE |
 | 2023-11-01 09:38:00 |         1 |     81 | ACTIVE   |
 | 2023-11-01 09:38:00 |         2 |     86 | ACTIVE   |
 | 2023-11-01 09:38:00 |         3 |     77 | ACTIVE   |
 +---------------------+-----------+--------+----------*/

The output table contains an aligned time series for each device and value columns (signal and state), computed using the gap-filling methods specified in the function call.

Join time series data

You can join time series data using a windowed join or AS OF join.

Windowed join

Sometimes you need to join two or more tables with time series data. Consider the following two tables:

mydataset.sensor_temperatures, contains temperature data reported by each sensor every 15 seconds.
mydataset.sensor_fuel_rates, contains the fuel consumption rate measured by each sensor every 15 seconds.

To create these tables, run the following queries:

CREATE OR REPLACE TABLE mydataset.sensor_temperatures AS
SELECT * FROM UNNEST(
  ARRAY<STRUCT<sensor_id INT64, ts TIMESTAMP, temp FLOAT64>>[
  (1, TIMESTAMP '2020-01-01 12:00:00.063', 37.1),
  (1, TIMESTAMP '2020-01-01 12:00:15.024', 37.2),
  (1, TIMESTAMP '2020-01-01 12:00:30.032', 37.3),
  (2, TIMESTAMP '2020-01-01 12:00:01.001', 38.1),
  (2, TIMESTAMP '2020-01-01 12:00:15.082', 38.2),
  (2, TIMESTAMP '2020-01-01 12:00:31.009', 38.3)
]);

CREATE OR REPLACE TABLE mydataset.sensor_fuel_rates AS
SELECT * FROM UNNEST(
  ARRAY<STRUCT<sensor_id INT64, ts TIMESTAMP, rate FLOAT64>>[
    (1, TIMESTAMP '2020-01-01 12:00:11.016', 10.1),
    (1, TIMESTAMP '2020-01-01 12:00:26.015', 10.2),
    (1, TIMESTAMP '2020-01-01 12:00:41.014', 10.3),
    (2, TIMESTAMP '2020-01-01 12:00:08.099', 11.1),
    (2, TIMESTAMP '2020-01-01 12:00:23.087', 11.2),
    (2, TIMESTAMP '2020-01-01 12:00:38.077', 11.3)
]);

The following is the actual data from the tables:

SELECT * FROM mydataset.sensor_temperatures ORDER BY sensor_id, ts;

 /*-----------+---------------------+------+
 | sensor_id |         ts          | temp |
 +-----------+---------------------+------+
 |         1 | 2020-01-01 12:00:00 | 37.1 |
 |         1 | 2020-01-01 12:00:15 | 37.2 |
 |         1 | 2020-01-01 12:00:30 | 37.3 |
 |         2 | 2020-01-01 12:00:01 | 38.1 |
 |         2 | 2020-01-01 12:00:15 | 38.2 |
 |         2 | 2020-01-01 12:00:31 | 38.3 |
 +-----------+---------------------+------*/

SELECT * FROM mydataset.sensor_fuel_rates ORDER BY sensor_id, ts;

 /*-----------+---------------------+------+
 | sensor_id |         ts          | rate |
 +-----------+---------------------+------+
 |         1 | 2020-01-01 12:00:11 | 10.1 |
 |         1 | 2020-01-01 12:00:26 | 10.2 |
 |         1 | 2020-01-01 12:00:41 | 10.3 |
 |         2 | 2020-01-01 12:00:08 | 11.1 |
 |         2 | 2020-01-01 12:00:23 | 11.2 |
 |         2 | 2020-01-01 12:00:38 | 11.3 |
 +-----------+---------------------+------*/

To check the fuel consumption rate at the temperature reported by each sensor, you can join the two time series.

Although the data in the two time series is unaligned, it is sampled at the same interval (15 seconds), therefore such data is a good candidate for windowed join. Use the time bucketing functions to align timestamps used as join keys.

The following queries illustrate how each timestamp can be assigned to 15-second windows using the TIMESTAMP_BUCKET function:

SELECT *, TIMESTAMP_BUCKET(ts, INTERVAL 15 SECOND) ts_window
FROM mydataset.sensor_temperatures
ORDER BY sensor_id, ts;

/*-----------+---------------------+------+---------------------+
 | sensor_id |         ts          | temp |      ts_window      |
 +-----------+---------------------+------+---------------------+
 |         1 | 2020-01-01 12:00:00 | 37.1 | 2020-01-01 12:00:00 |
 |         1 | 2020-01-01 12:00:15 | 37.2 | 2020-01-01 12:00:15 |
 |         1 | 2020-01-01 12:00:30 | 37.3 | 2020-01-01 12:00:30 |
 |         2 | 2020-01-01 12:00:01 | 38.1 | 2020-01-01 12:00:00 |
 |         2 | 2020-01-01 12:00:15 | 38.2 | 2020-01-01 12:00:15 |
 |         2 | 2020-01-01 12:00:31 | 38.3 | 2020-01-01 12:00:30 |
 +-----------+---------------------+------+---------------------*/

SELECT *, TIMESTAMP_BUCKET(ts, INTERVAL 15 SECOND) ts_window
FROM mydataset.sensor_fuel_rates
ORDER BY sensor_id, ts;

/*-----------+---------------------+------+---------------------+
 | sensor_id |         ts          | rate |      ts_window      |
 +-----------+---------------------+------+---------------------+
 |         1 | 2020-01-01 12:00:11 | 10.1 | 2020-01-01 12:00:00 |
 |         1 | 2020-01-01 12:00:26 | 10.2 | 2020-01-01 12:00:15 |
 |         1 | 2020-01-01 12:00:41 | 10.3 | 2020-01-01 12:00:30 |
 |         2 | 2020-01-01 12:00:08 | 11.1 | 2020-01-01 12:00:00 |
 |         2 | 2020-01-01 12:00:23 | 11.2 | 2020-01-01 12:00:15 |
 |         2 | 2020-01-01 12:00:38 | 11.3 | 2020-01-01 12:00:30 |
 +-----------+---------------------+------+---------------------*/

You can use this concept to join the fuel consumption rate data with the temperature reported by each sensor:

SELECT
  t1.sensor_id AS sensor_id,
  t1.ts AS temp_ts,
  t1.temp AS temp,
  t2.ts AS rate_ts,
  t2.rate AS rate
FROM mydataset.sensor_temperatures t1
LEFT JOIN mydataset.sensor_fuel_rates t2
ON TIMESTAMP_BUCKET(t1.ts, INTERVAL 15 SECOND) =
     TIMESTAMP_BUCKET(t2.ts, INTERVAL 15 SECOND)
   AND t1.sensor_id = t2.sensor_id
ORDER BY sensor_id, temp_ts;

/*-----------+---------------------+------+---------------------+------+
 | sensor_id |       temp_ts       | temp |       rate_ts       | rate |
 +-----------+---------------------+------+---------------------+------+
 |         1 | 2020-01-01 12:00:00 | 37.1 | 2020-01-01 12:00:11 | 10.1 |
 |         1 | 2020-01-01 12:00:15 | 37.2 | 2020-01-01 12:00:26 | 10.2 |
 |         1 | 2020-01-01 12:00:30 | 37.3 | 2020-01-01 12:00:41 | 10.3 |
 |         2 | 2020-01-01 12:00:01 | 38.1 | 2020-01-01 12:00:08 | 11.1 |
 |         2 | 2020-01-01 12:00:15 | 38.2 | 2020-01-01 12:00:23 | 11.2 |
 |         2 | 2020-01-01 12:00:31 | 38.3 | 2020-01-01 12:00:38 | 11.3 |
 +-----------+---------------------+------+---------------------+------*/

`AS OF` join

For this section, use the mydataset.sensor_temperatures table and create a new table, mydataset.sensor_location.

The mydataset.sensor_temperatures table contains temperature data from different sensors, reported every 15 seconds:

SELECT * FROM mydataset.sensor_temperatures ORDER BY sensor_id, ts;

/*-----------+---------------------+------+
 | sensor_id |         ts          | temp |
 +-----------+---------------------+------+
 |         1 | 2020-01-01 12:00:00 | 37.1 |
 |         1 | 2020-01-01 12:00:15 | 37.2 |
 |         1 | 2020-01-01 12:00:30 | 37.3 |
 |         2 | 2020-01-01 12:00:45 | 38.1 |
 |         2 | 2020-01-01 12:01:01 | 38.2 |
 |         2 | 2020-01-01 12:01:15 | 38.3 |
 +-----------+---------------------+------*/

To create mydataset.sensor_location, run the following query:

CREATE OR REPLACE TABLE mydataset.sensor_locations AS
SELECT * FROM UNNEST(
  ARRAY<STRUCT<sensor_id INT64, ts TIMESTAMP, location GEOGRAPHY>>[
  (1, TIMESTAMP '2020-01-01 11:59:47.063', ST_GEOGPOINT(-122.022, 37.406)),
  (1, TIMESTAMP '2020-01-01 12:00:08.185', ST_GEOGPOINT(-122.021, 37.407)),
  (1, TIMESTAMP '2020-01-01 12:00:28.032', ST_GEOGPOINT(-122.020, 37.405)),
  (2, TIMESTAMP '2020-01-01 07:28:41.239', ST_GEOGPOINT(-122.390, 37.790))
]);

/*-----------+---------------------+------------------------+
 | sensor_id |         ts          |        location        |
 +-----------+---------------------+------------------------+
 |         1 | 2020-01-01 11:59:47 | POINT(-122.022 37.406) |
 |         1 | 2020-01-01 12:00:08 | POINT(-122.021 37.407) |
 |         1 | 2020-01-01 12:00:28 |  POINT(-122.02 37.405) |
 |         2 | 2020-01-01 07:28:41 |   POINT(-122.39 37.79) |
 +-----------+---------------------+------------------------*/

Now join data from mydataset.sensor_temperatures with data from mydataset.sensor_location.

In this scenario, you can't use a windowed join, since the temperature data and location date are not reported at the same interval.

One way to do this in BigQuery is to transform the timestamp data into a range, using the RANGE data type. The range represents the temporal validity of a row, providing the start and end time for which the row is valid.

Use the LEAD window function to find the next data point in the time series, relative to the current data point, which is also the end-boundary of the temporal validity of the current row. The following queries demonstrate this, converting location data to validity ranges:

WITH locations_ranges AS (
  SELECT
    sensor_id,
    RANGE(ts, LEAD(ts) OVER (PARTITION BY sensor_id ORDER BY ts ASC)) AS ts_range,
    location
  FROM mydataset.sensor_locations
)
SELECT * FROM locations_ranges ORDER BY sensor_id, ts_range;

/*-----------+--------------------------------------------+------------------------+
 | sensor_id |                  ts_range                  |        location        |
 +-----------+--------------------------------------------+------------------------+
 |         1 | [2020-01-01 11:59:47, 2020-01-01 12:00:08) | POINT(-122.022 37.406) |
 |         1 | [2020-01-01 12:00:08, 2020-01-01 12:00:28) | POINT(-122.021 37.407) |
 |         1 |           [2020-01-01 12:00:28, UNBOUNDED) |  POINT(-122.02 37.405) |
 |         2 |           [2020-01-01 07:28:41, UNBOUNDED) |   POINT(-122.39 37.79) |
 +-----------+--------------------------------------------+------------------------*/

Now you can join temperatures data (left) with the location data (right):

WITH locations_ranges AS (
  SELECT
    sensor_id,
    RANGE(ts, LEAD(ts) OVER (PARTITION BY sensor_id ORDER BY ts ASC)) AS ts_range,
    location
  FROM mydataset.sensor_locations
)
SELECT
  t1.sensor_id AS sensor_id,
  t1.ts AS temp_ts,
  t1.temp AS temp,
  t2.location AS location
FROM mydataset.sensor_temperatures t1
LEFT JOIN locations_ranges t2
ON RANGE_CONTAINS(t2.ts_range, t1.ts)
AND t1.sensor_id = t2.sensor_id
ORDER BY sensor_id, temp_ts;

/*-----------+---------------------+------+------------------------+
 | sensor_id |       temp_ts       | temp |        location        |
 +-----------+---------------------+------+------------------------+
 |         1 | 2020-01-01 12:00:00 | 37.1 | POINT(-122.022 37.406) |
 |         1 | 2020-01-01 12:00:15 | 37.2 | POINT(-122.021 37.407) |
 |         1 | 2020-01-01 12:00:30 | 37.3 |  POINT(-122.02 37.405) |
 |         2 | 2020-01-01 12:00:01 | 38.1 |   POINT(-122.39 37.79) |
 |         2 | 2020-01-01 12:00:15 | 38.2 |   POINT(-122.39 37.79) |
 |         2 | 2020-01-01 12:00:31 | 38.3 |   POINT(-122.39 37.79) |
 +-----------+---------------------+------+------------------------*/

Combine and split range data

In this section, combine range data that have overlapping ranges and split range data into smaller ranges.

Combine range data

Tables with range values might have overlapping ranges. In the following query, the time ranges capture the state of sensors at approximately 5-minute intervals:

CREATE OR REPLACE TABLE mydataset.sensor_metrics AS
SELECT * FROM UNNEST(
  ARRAY<STRUCT<sensor_id INT64, duration RANGE<DATETIME>, flow INT64, spins INT64>>[
  (1, RANGE<DATETIME> "[2020-01-01 12:00:01, 2020-01-01 12:05:23)", 10, 1),
  (1, RANGE<DATETIME> "[2020-01-01 12:05:12, 2020-01-01 12:10:46)", 10, 20),
  (1, RANGE<DATETIME> "[2020-01-01 12:10:27, 2020-01-01 12:15:56)", 11, 4),
  (1, RANGE<DATETIME> "[2020-01-01 12:16:00, 2020-01-01 12:20:58)", 11, 9),
  (1, RANGE<DATETIME> "[2020-01-01 12:20:33, 2020-01-01 12:25:08)", 11, 8),
  (2, RANGE<DATETIME> "[2020-01-01 12:00:19, 2020-01-01 12:05:08)", 21, 31),
  (2, RANGE<DATETIME> "[2020-01-01 12:05:08, 2020-01-01 12:10:30)", 21, 2),
  (2, RANGE<DATETIME> "[2020-01-01 12:10:22, 2020-01-01 12:15:42)", 21, 10)
]);

The following query on the table shows several overlapping ranges:

SELECT * FROM mydataset.sensor_metrics;

/*-----------+--------------------------------------------+------+-------+
 | sensor_id |                  duration                  | flow | spins |
 +-----------+--------------------------------------------+------+-------+
 |         1 | [2020-01-01 12:00:01, 2020-01-01 12:05:23) | 10   |     1 |
 |         1 | [2020-01-01 12:05:12, 2020-01-01 12:10:46) | 10   |    20 |
 |         1 | [2020-01-01 12:10:27, 2020-01-01 12:15:56) | 11   |     4 |
 |         1 | [2020-01-01 12:16:00, 2020-01-01 12:20:58) | 11   |     9 |
 |         1 | [2020-01-01 12:20:33, 2020-01-01 12:25:08) | 11   |     8 |
 |         2 | [2020-01-01 12:00:19, 2020-01-01 12:05:08) | 21   |    31 |
 |         2 | [2020-01-01 12:05:08, 2020-01-01 12:10:30) | 21   |     2 |
 |         2 | [2020-01-01 12:10:22, 2020-01-01 12:15:42) | 21   |    10 |
 +-----------+--------------------------------------------+------+-------*/

For some of the overlapping ranges, the value in the flow column is the same. For example, rows 1 and 2 overlap, and also have the same flow readings. You can combine these two rows to reduce the number of rows in the table. You can use the RANGE_SESSIONIZE table function to find ranges that overlap with each row, and provide an additional session_range column that contains a range that is the union of all ranges that overlap. To display the session ranges for each row, run the following query:

SELECT sensor_id, session_range, flow
FROM RANGE_SESSIONIZE(
  # Input data.
  (SELECT sensor_id, duration, flow FROM mydataset.sensor_metrics),
  # Range column.
  "duration",
  # Partitioning columns. Ranges are sessionized only within these partitions.
  ["sensor_id", "flow"],
  # Sessionize mode.
  "OVERLAPS")
ORDER BY sensor_id, session_range;

/*-----------+--------------------------------------------+------+
 | sensor_id |                session_range               | flow |
 +-----------+--------------------------------------------+------+
 |         1 | [2020-01-01 12:00:01, 2020-01-01 12:10:46) | 10   |
 |         1 | [2020-01-01 12:00:01, 2020-01-01 12:10:46) | 10   |
 |         1 | [2020-01-01 12:10:27, 2020-01-01 12:15:56) | 11   |
 |         1 | [2020-01-01 12:16:00, 2020-01-01 12:25:08) | 11   |
 |         1 | [2020-01-01 12:16:00, 2020-01-01 12:25:08) | 11   |
 |         2 | [2020-01-01 12:00:19, 2020-01-01 12:05:08) | 21   |
 |         2 | [2020-01-01 12:05:08, 2020-01-01 12:15:42) | 21   |
 |         2 | [2020-01-01 12:05:08, 2020-01-01 12:15:42) | 21   |
 +-----------+--------------------------------------------+------*/

Note that for sensor_id having value 2, the first row's end boundary has the same datetime value as the second row's start boundary. However, because end boundaries are exclusive, they don't overlap (only meet) and hence were not in the same session ranges. If you want to place these two rows in the same session ranges, use the MEETS sessionize mode.

To combine the ranges, group the results by session_range and the partitioning columns (sensor_id and flow):

SELECT sensor_id, session_range, flow
FROM RANGE_SESSIONIZE(
  (SELECT sensor_id, duration, flow FROM mydataset.sensor_metrics),
  "duration",
  ["sensor_id", "flow"],
  "OVERLAPS")
GROUP BY sensor_id, session_range, flow
ORDER BY sensor_id, session_range;

/*-----------+--------------------------------------------+------+
 | sensor_id |                session_range               | flow |
 +-----------+--------------------------------------------+------+
 |         1 | [2020-01-01 12:00:01, 2020-01-01 12:10:46) | 10   |
 |         1 | [2020-01-01 12:10:27, 2020-01-01 12:15:56) | 11   |
 |         1 | [2020-01-01 12:16:00, 2020-01-01 12:25:08) | 11   |
 |         2 | [2020-01-01 12:00:19, 2020-01-01 12:05:08) | 21   |
 |         2 | [2020-01-01 12:05:08, 2020-01-01 12:15:42) | 21   |
 +-----------+--------------------------------------------+------*/

Finally, add the spins column in the session data by aggregating it using SUM.

SELECT sensor_id, session_range, flow, SUM(spins) as spins
FROM RANGE_SESSIONIZE(
  TABLE mydataset.sensor_metrics,
  "duration",
  ["sensor_id", "flow"],
  "OVERLAPS")
GROUP BY sensor_id, session_range, flow
ORDER BY sensor_id, session_range;

/*-----------+--------------------------------------------+------+-------+
 | sensor_id |                session_range               | flow | spins |
 +-----------+--------------------------------------------+------+-------+
 |         1 | [2020-01-01 12:00:01, 2020-01-01 12:10:46) | 10   |    21 |
 |         1 | [2020-01-01 12:10:27, 2020-01-01 12:15:56) | 11   |     4 |
 |         1 | [2020-01-01 12:16:00, 2020-01-01 12:25:08) | 11   |    17 |
 |         2 | [2020-01-01 12:00:19, 2020-01-01 12:05:08) | 21   |    31 |
 |         2 | [2020-01-01 12:05:08, 2020-01-01 12:15:42) | 21   |    12 |
 +-----------+--------------------------------------------+------+-------*/

Split range data

You can also split a range into smaller ranges. For this example, use the following table with range data:

/*-----------+--------------------------+------+-------+
 | sensor_id |         duration         | flow | spins |
 +-----------+--------------------------+------+-------+
 |         1 | [2020-01-01, 2020-12-31) | 10   |    21 |
 |         1 | [2021-01-01, 2021-12-31) | 11   |     4 |
 |         2 | [2020-04-15, 2021-04-15) | 21   |    31 |
 |         2 | [2021-04-15, 2021-04-15) | 21   |    12 |
 +-----------+--------------------------+------+-------*/

Now, split the original ranges into 3-month intervals:

WITH sensor_data AS (
  SELECT * FROM UNNEST(
    ARRAY<STRUCT<sensor_id INT64, duration RANGE<DATE>, flow INT64, spins INT64>>[
    (1, RANGE<DATE> "[2020-01-01, 2020-12-31)", 10, 21),
    (1, RANGE<DATE> "[2021-01-01, 2021-12-31)", 11, 4),
    (2, RANGE<DATE> "[2020-04-15, 2021-04-15)", 21, 31),
    (2, RANGE<DATE> "[2021-04-15, 2022-04-15)", 21, 12)
  ])
)
SELECT sensor_id, expanded_range, flow, spins
FROM sensor_data, UNNEST(GENERATE_RANGE_ARRAY(duration, INTERVAL 3 MONTH)) AS expanded_range;

/*-----------+--------------------------+------+-------+
 | sensor_id |      expanded_range      | flow | spins |
 +-----------+--------------------------+------+-------+
 |         1 | [2020-01-01, 2020-04-01) |   10 |    21 |
 |         1 | [2020-04-01, 2020-07-01) |   10 |    21 |
 |         1 | [2020-07-01, 2020-10-01) |   10 |    21 |
 |         1 | [2020-10-01, 2020-12-31) |   10 |    21 |
 |         1 | [2021-01-01, 2021-04-01) |   11 |     4 |
 |         1 | [2021-04-01, 2021-07-01) |   11 |     4 |
 |         1 | [2021-07-01, 2021-10-01) |   11 |     4 |
 |         1 | [2021-10-01, 2021-12-31) |   11 |     4 |
 |         2 | [2020-04-15, 2020-07-15) |   21 |    31 |
 |         2 | [2020-07-15, 2020-10-15) |   21 |    31 |
 |         2 | [2020-10-15, 2021-01-15) |   21 |    31 |
 |         2 | [2021-01-15, 2021-04-15) |   21 |    31 |
 |         2 | [2021-04-15, 2021-07-15) |   21 |    12 |
 |         2 | [2021-07-15, 2021-10-15) |   21 |    12 |
 |         2 | [2021-10-15, 2022-01-15) |   21 |    12 |
 |         2 | [2022-01-15, 2022-04-15) |   21 |    12 |
 +-----------+--------------------------+------+-------*/

In the previous query, each original range was broken down into smaller ranges, with width set to INTERVAL 3 MONTH. However, the 3-month ranges are not aligned to a common origin. To align these ranges to a common origin 2020-01-01, run the following query:

WITH sensor_data AS (
  SELECT * FROM UNNEST(
    ARRAY<STRUCT<sensor_id INT64, duration RANGE<DATE>, flow INT64, spins INT64>>[
    (1, RANGE<DATE> "[2020-01-01, 2020-12-31)", 10, 21),
    (1, RANGE<DATE> "[2021-01-01, 2021-12-31)", 11, 4),
    (2, RANGE<DATE> "[2020-04-15, 2021-04-15)", 21, 31),
    (2, RANGE<DATE> "[2021-04-15, 2022-04-15)", 21, 12)
  ])
)
SELECT sensor_id, expanded_range, flow, spins
FROM sensor_data
JOIN UNNEST(GENERATE_RANGE_ARRAY(RANGE<DATE> "[2020-01-01, 2022-12-31)", INTERVAL 3 MONTH)) AS expanded_range
ON RANGE_OVERLAPS(duration, expanded_range);

/*-----------+--------------------------+------+-------+
 | sensor_id |      expanded_range      | flow | spins |
 +-----------+--------------------------+------+-------+
 |         1 | [2020-01-01, 2020-04-01) |   10 |    21 |
 |         1 | [2020-04-01, 2020-07-01) |   10 |    21 |
 |         1 | [2020-07-01, 2020-10-01) |   10 |    21 |
 |         1 | [2020-10-01, 2021-01-01) |   10 |    21 |
 |         1 | [2021-01-01, 2021-04-01) |   11 |     4 |
 |         1 | [2021-04-01, 2021-07-01) |   11 |     4 |
 |         1 | [2021-07-01, 2021-10-01) |   11 |     4 |
 |         1 | [2021-10-01, 2022-01-01) |   11 |     4 |
 |         2 | [2020-04-01, 2020-07-01) |   21 |    31 |
 |         2 | [2020-07-01, 2020-10-01) |   21 |    31 |
 |         2 | [2020-10-01, 2021-01-01) |   21 |    31 |
 |         2 | [2021-01-01, 2021-04-01) |   21 |    31 |
 |         2 | [2021-04-01, 2021-07-01) |   21 |    31 |
 |         2 | [2021-04-01, 2021-07-01) |   21 |    12 |
 |         2 | [2021-07-01, 2021-10-01) |   21 |    12 |
 |         2 | [2021-10-01, 2022-01-01) |   21 |    12 |
 |         2 | [2022-01-01, 2022-04-01) |   21 |    12 |
 |         2 | [2022-04-01, 2022-07-01) |   21 |    12 |
 +-----------+--------------------------+------+-------*/

In the previous query, the row with the range [2020-04-15, 2021-04-15) is split into 5 ranges, starting with the range [2020-04-01, 2020-07-01). Note that the start boundary now extends beyond the original start boundary, in order to align with the common origin. If you don't want the start boundary to not extend beyond the original start boundary, you can restrict the JOIN condition:

WITH sensor_data AS (
  SELECT * FROM UNNEST(
    ARRAY<STRUCT<sensor_id INT64, duration RANGE<DATE>, flow INT64, spins INT64>>[
    (1, RANGE<DATE> "[2020-01-01, 2020-12-31)", 10, 21),
    (1, RANGE<DATE> "[2021-01-01, 2021-12-31)", 11, 4),
    (2, RANGE<DATE> "[2020-04-15, 2021-04-15)", 21, 31),
    (2, RANGE<DATE> "[2021-04-15, 2022-04-15)", 21, 12)
  ])
)
SELECT sensor_id, expanded_range, flow, spins
FROM sensor_data
JOIN UNNEST(GENERATE_RANGE_ARRAY(RANGE<DATE> "[2020-01-01, 2022-12-31)", INTERVAL 3 MONTH)) AS expanded_range
ON RANGE_CONTAINS(duration, RANGE_START(expanded_range));

/*-----------+--------------------------+------+-------+
 | sensor_id |      expanded_range      | flow | spins |
 +-----------+--------------------------+------+-------+
 |         1 | [2020-01-01, 2020-04-01) |   10 |    21 |
 |         1 | [2020-04-01, 2020-07-01) |   10 |    21 |
 |         1 | [2020-07-01, 2020-10-01) |   10 |    21 |
 |         1 | [2020-10-01, 2021-01-01) |   10 |    21 |
 |         1 | [2021-01-01, 2021-04-01) |   11 |     4 |
 |         1 | [2021-04-01, 2021-07-01) |   11 |     4 |
 |         1 | [2021-07-01, 2021-10-01) |   11 |     4 |
 |         1 | [2021-10-01, 2022-01-01) |   11 |     4 |
 |         2 | [2020-07-01, 2020-10-01) |   21 |    31 |
 |         2 | [2020-10-01, 2021-01-01) |   21 |    31 |
 |         2 | [2021-01-01, 2021-04-01) |   21 |    31 |
 |         2 | [2021-04-01, 2021-07-01) |   21 |    31 |
 |         2 | [2021-07-01, 2021-10-01) |   21 |    12 |
 |         2 | [2021-10-01, 2022-01-01) |   21 |    12 |
 |         2 | [2022-01-01, 2022-04-01) |   21 |    12 |
 |         2 | [2022-04-01, 2022-07-01) |   21 |    12 |
 +-----------+--------------------------+------+-------*/

You now see that the range [2020-04-15, 2021-04-15) was split into 4 ranges, starting with the range [2020-07-01, 2020-10-01).

Best practices for storing data

When storing time series data, it is important to consider the query patterns that are used against the tables where the data is stored. Typically, when querying time series data, you can filter the data for a specific time range.
To optimize these usage patterns, it is recommended to store time series data in partitioned tables, with data partitioned either by the time column or ingestion time. This can significantly improve the query time performance of the time series data, as this lets BigQuery to prune partitions that don't contain queried data.
You can enable clustering on the time, range, or one of the partitioning columns for further query time performance improvements.