time_weight() functions

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Calculate time-weighted summary statistics, such as averages (means) and integrals. Time weighting is used when data is unevenly sampled over time. In that case, a straight average gives misleading results, as it biases towards more frequently sampled values.

For example, a sensor might silently spend long periods of time in a steady state, and send data only when a significant change occurs. The regular mean counts the steady-state reading as only a single point, whereas a time-weighted mean accounts for the long period of time spent in the steady state. In essence, the time-weighted mean takes an integral over time, then divides by the elapsed time.

This group of functions uses the two-step aggregation pattern.

Rather than calculating the final result in one step, you first create an intermediate aggregate by using the aggregate function.

Then, use any of the accessors on the intermediate aggregate to calculate a final result. You can also roll up multiple intermediate aggregates with the rollup functions.

The two-step aggregation pattern has several advantages:

More efficient because multiple accessors can reuse the same aggregate
Easier to reason about performance, because aggregation is separate from final computation
Easier to understand when calculations can be rolled up into larger intervals, especially in window functions and continuous aggregates
Can perform retrospective analysis even when underlying data is dropped, because the intermediate aggregate stores extra information not available in the final result

To learn more, see the blog post on two-step aggregates.

Functions in this group

time_weight: Aggregate data into an intermediate time-weighted aggregate form for further calculation

average: Calculate the time-weighted average of values in a TimeWeightSummary
first_time: Get the first timestamp from a TimeWeightSummary aggregate
first_val: Get the first value from a TimeWeightSummary aggregate
integral: Calculate the integral from a TimeWeightSummary
interpolated_average: Calculate the time-weighted average over an interval, while interpolating the interval bounds
interpolated_integral: Calculate the integral over an interval, while interpolating the interval bounds
last_time: Get the last timestamp from a TimeWeightSummary aggregate
last_val: Get the last value from a TimeWeightSummary aggregate

rollup: Combine multiple TimeWeightSummaries

Function details

time_weight(
    method TEXT,
    ts TIMESTAMPTZ,
    value DOUBLE PRECISION
) RETURNS TimeWeightSummary

This is the first step for performing any time-weighted calculations. Use time_weight to create an intermediate aggregate (TimeWeightSummary) from your data. This intermediate form can then be used by one or more accessors in this group to compute final results. Optionally, multiple such intermediate aggregate objects can be combined using rollup() before an accessor is applied.

Required arguments

Name	Type	Description
`method`	`TEXT`	The weighting method to use. The available methods are `linear` (or its alias `trapezoidal`, for those familiar with numeric integration methods) and `LOCF`, which stands for 'last observation carried forward'. `linear` fills in missing data by interpolating linearly between the start and end points of the gap. `LOCF` fills in the gap by assuming that the value remains constant until the next value is seen. `LOCF` is most useful when a measurement is taken only when a value changes. `linear` is most useful if there are no such guarantees on the measurement. The method names are case-insensitive.
`ts`	`TIMESTAMPTZ`	The time at each point. Null values are ignored. An aggregate evaluated on only `null` values returns `null`.
`value`	`DOUBLE PRECISION`	The value at each point to use for the time-weighted aggregate. Null values are ignored. An aggregate evaluated on only `null` values returns `null`.

Returns

Column	Type	Description
`time_weight`	`TimeWeightSummary`	A `TimeWeightSummary` object that can be passed to other functions within the time-weighting API

Examples

Aggregate data from column val into daily time-weighted aggregates, using the linear interpolation method:


SELECT
    time_bucket('1 day'::interval, ts) as dt,
    time_weight('Linear', ts, val) AS tw
FROM foo
GROUP BY time_bucket('1 day'::interval, ts)

average(
    tws TimeWeightSummary
) RETURNS DOUBLE PRECISION

Calculate the time-weighted average. Equal to integral divided by the elapsed time.

Required arguments

Name	Type	Description
`tws`	`TimeWeightSummary`	The input `TimeWeightSummary` from a `time_weight()` call.

Returns

Column	Type	Description
`average`	`DOUBLE PRECISION`	The time-weighted average.

Examples

Calculate the time-weighted average of the column val, using the 'last observation carried forward' interpolation method:


SELECT
    id,
    average(tws)
FROM (
    SELECT
        id,
        time_weight('LOCF', ts, val) AS tws
    FROM foo
    GROUP BY id
) t

first_time(
    tw TimeWeightSummary
) RETURNS TIMESTAMPTZ

Get the timestamp of the first point in a TimeWeightSummary aggregate.

Required arguments

Name	Type	Description
`tws`	`TimeWeightSummary`	The input `TimeWeightSummary` from a `time_weight()` call.

Returns

Column	Type	Description
`first_time`	`TIMESTAMPTZ`	The time of the first point in the `TimeWeightSummary`

Examples

Produce a linear TimeWeightSummary over the column val and get the first timestamp:


WITH t as (
    SELECT
        time_bucket('1 day'::interval, ts) as dt,
        time_weight('Linear', ts, val) AS tw
    FROM table
    GROUP BY time_bucket('1 day'::interval, ts)
)
SELECT
    dt,
    first_time(tw)
FROM t;

first_val(
    tw TimeWeightSummary
) RETURNS DOUBLE PRECISION

Get the value of the first point in a TimeWeightSummary aggregate.

Required arguments

Name	Type	Description
`tws`	`TimeWeightSummary`	The input `TimeWeightSummary` from a `time_weight()` call.

Returns

Column	Type	Description
`first_val`	`DOUBLE PRECISION`	The value of the first point in the `TimeWeightSummary`

Examples

Produce a linear TimeWeightSummary over the column val and get the first value:


WITH t as (
    SELECT
        time_bucket('1 day'::interval, ts) as dt,
        time_weight('Linear', ts, val) AS tw
    FROM table
    GROUP BY time_bucket('1 day'::interval, ts)
)
SELECT
    dt,
    first_val(tw)
FROM t;

integral(
    tws TimeWeightSummary
    [, unit TEXT]
) RETURNS DOUBLE PRECISION

Calculate the integral, or the area under the curve formed by the data points. Equal to average multiplied by the elapsed time.

Required arguments

Name	Type	Description
`tws`	`TimeWeightSummary`	The input `TimeWeightSummary` from a `time_weight()` call.

Optional arguments

Name	Type	Description
`unit`	`TEXT`	The unit of time to express the integral in. Can be `microsecond`, `millisecond`, `second`, `minute`, `hour`, or any alias for those units supported by PostgreSQL. Defaults to `second`.

Returns

Column	Type	Description
`integral`	`DOUBLE PRECISION`	The time-weighted integral.

Examples

Create a table to track irregularly sampled storage usage in bytes, and get the total storage used in byte-hours. Use the 'last observation carried forward' interpolation method:


-- Create a table to track irregularly sampled storage usage
CREATE TABLE user_storage_usage(ts TIMESTAMP, storage_bytes BIGINT);
INSERT INTO user_storage_usage(ts, storage_bytes) VALUES
    ('01-01-2022 00:00', 0),
    ('01-01-2022 00:30', 100),
    ('01-01-2022 03:00', 300),
    ('01-01-2022 03:10', 1000),
    ('01-01-2022 03:25', 817);

-- Get the total byte-hours used
SELECT
    integral(time_weight('LOCF', ts, storage_bytes), 'hours')
FROM
    user_storage_usage;

interpolated_average(
    tws TimeWeightSummary,
    start TIMESTAMPTZ,
    interval INTERVAL
    [, prev TimeWeightSummary]
    [, next TimeWeightSummary]
) RETURNS DOUBLE PRECISION

Calculate the time-weighted average over an interval, while interpolating the interval bounds.

Similar to average, but allows an accurate calculation across interval bounds when data has been bucketed into separate time intervals, and there is no data point precisely at the interval bound. For example, this is useful in a window function.

Values from the previous and next buckets are used to interpolate the values at the bounds, using the same interpolation method used within the TimeWeightSummary itself.

Equal to interpolated_integral divided by the elapsed time.

Required arguments

Name	Type	Description
`tws`	`TimeWeightSummary`	The input `TimeWeightSummary` from a `time_weight()` call.
`start`	`TIMESTAMPTZ`	The start of the interval which the time-weighted average should cover (if there is a preceeding point).
`interval`	`INTERVAL`	The length of the interval which the time-weighted average should cover.

Optional arguments

Name	Type	Description
`prev`	`TimeWeightSummary`	The `TimeWeightSummary` from the prior interval, used to interpolate the value at `start`. If NULL, the first timestamp in `tws` is used for the starting value. The prior interval can be determined from the PostgreSQL `lag()` function.
`next`	`TimeWeightSummary`	The `TimeWeightSummary` from the next interval, used to interpolate the value at `start` + `interval`. If NULL, the first timestamp in `tws` is used for the starting value. The next interval can be determined from the PostgreSQL `lead()` function.

Returns

Column	Type	Description
`average`	`DOUBLE PRECISION`	The time-weighted average for the interval (`start`, `start` + `interval`), computed from the `TimeWeightSummary` plus end points interpolated from `prev` and `next`

Examples

Calculate the time-weighted daily average of the column val, interpolating over bucket bounds using the 'last observation carried forward' method:


SELECT
    id,
    time,
    interpolated_average(
        tws,
        time,
        '1 day',
        LAG(tws) OVER (PARTITION BY id ORDER by time),
        LEAD(tws) OVER (PARTITION BY id ORDER by time)
    )
FROM (
    SELECT
        id,
        time_bucket('1 day', ts) AS time,
        time_weight('LOCF', ts, val) AS tws
    FROM foo
    GROUP BY id, time
) t

interpolated_integral(
    tws TimeWeightSummary,
    start TIMESTAMPTZ,
    interval INTERVAL
    [, prev TimeWeightSummary]
    [, next TimeWeightSummary]
    [, unit TEXT]
) RETURNS DOUBLE PRECISION

Calculate the integral over an interval, while interpolating the interval bounds.

Similar to integral, but allows an accurate calculation across interval bounds when data has been bucketed into separate time intervals, and there is no data point precisely at the interval bound. For example, this is useful in a window function.

Values from the previous and next buckets are used to interpolate the values at the bounds, using the same interpolation method used within the TimeWeightSummary itself.

Equal to interpolated_average multiplied by the elapsed time.

Required arguments

Name	Type	Description
`tws`	`TimeWeightSummary`	The input `TimeWeightSummary` from a `time_weight()` call.
`start`	`TIMESTAMPTZ`	The start of the interval which the time-weighted integral should cover (if there is a preceding point).
`interval`	`INTERVAL`	The length of the interval which the time-weighted integral should cover.

Optional arguments

Name	Type	Description
`prev`	`TimeWeightSummary`	The `TimeWeightSummary` from the prior interval, used to interpolate the value at `start`. If NULL, the first timestamp in `tws` is used for the starting value. The prior interval can be determined from the PostgreSQL `lag()` function.
`next`	`TimeWeightSummary`	The `TimeWeightSummary` from the next interval, used to interpolate the value at `start` + `interval`. If NULL, the first timestamp in `tws` is used for the starting value. The next interval can be determined from the PostgreSQL `lead()` function.
`unit`	`TEXT`	The unit of time to express the integral in. Can be `microsecond`, `millisecond`, `second`, `minute`, `hour`, or any alias for those units supported by PostgreSQL. Defaults to `second`.

Returns

Column	Type	Description
`integral`	`DOUBLE PRECISION`	The time-weighted integral for the interval (`start`, `start` + `interval`), computed from the `TimeWeightSummary` plus end points interpolated from `prev` and `next`

Examples

Create a table to track irregularly sampled storage usage in bytes, and get the total storage used in byte-hours between January 1 and January 6. Use the 'last observation carried forward' interpolation method:


-- Create a table to track irregularly sampled storage usage
CREATE TABLE user_storage_usage(ts TIMESTAMP, storage_bytes BIGINT);
INSERT INTO user_storage_usage(ts, storage_bytes) VALUES
    ('01-01-2022 20:55', 27),
    ('01-02-2022 18:33', 100),
    ('01-03-2022 03:05', 300),
    ('01-04-2022 12:13', 1000),
    ('01-05-2022 07:26', 817);


-- Get the total byte-hours used between Jan. 1 and Jan. 6
SELECT
    interpolated_integral(
        time_weight('LOCF', ts, storage_bytes),
        '01-01-2022',
        '5 days',
        NULL,
        NULL,
        'hours'
    )
FROM
    user_storage_usage;

last_time(
    tw TimeWeightSummary
) RETURNS TIMESTAMPTZ

Get the timestamp of the last point in a TimeWeightSummary aggregate.

Required arguments

Name	Type	Description
`tws`	`TimeWeightSummary`	The input `TimeWeightSummary` from a `time_weight()` call.

Returns

Column	Type	Description
`last_time`	`TIMESTAMPTZ`	The time of the last point in the `TimeWeightSummary`

Examples

Produce a linear TimeWeightSummary over the column val and get the last timestamp:


WITH t as (
    SELECT
        time_bucket('1 day'::interval, ts) as dt,
        time_weight('Linear', ts, val) AS tw
    FROM table
    GROUP BY time_bucket('1 day'::interval, ts)
)
SELECT
    dt,
    last_time(tw)
FROM t;

last_val(
    tw TimeWeightSummary
) RETURNS DOUBLE PRECISION

Get the value of the last point in a TimeWeightSummary aggregate.

Required arguments

Name	Type	Description
`tws`	`TimeWeightSummary`	The input `TimeWeightSummary` from a `time_weight()` call.

Returns

Column	Type	Description
`last_val`	`DOUBLE PRECISION`	The value of the last point in the `TimeWeightSummary`

Examples

Produce a linear TimeWeightSummary over the column val and get the last value:


WITH t as (
    SELECT
        time_bucket('1 day'::interval, ts) as dt,
        time_weight('Linear', ts, val) AS tw
    FROM table
    GROUP BY time_bucket('1 day'::interval, ts)
)
SELECT
    dt,
    last_val(tw)
FROM t;

rollup(
    tws TimeWeightSummary
) RETURNS TimeWeightSummary

Combine multiple intermediate time-weighted aggregate (TimeWeightSummary) objects produced by time_weight() into a single intermediate TimeWeightSummary object. For example, you can use rollup to combine time-weighted aggregates from 15-minute buckets into daily buckets.

Required arguments

Name	Type	Description
`time_weight`	`TimeWeightSummary`	The `TimeWeightSummary` aggregate produced by a `time_weight` call

Returns

Column	Type	Description
`rollup`	`StatsSummary1D`	A new `TimeWeightSummary` aggregate produced by combining the input `TimeWeightSummary` aggregates

Extended examples

Aggregate data into a `TimeWeightSummary` and calculate the average

Given a table foo with data in a column val, aggregate data into a daily TimeWeightSummary. Use that to calculate the average for column val:


WITH t as (
    SELECT
        time_bucket('1 day'::interval, ts) as dt,
        time_weight('Linear', ts, val) AS tw
    FROM foo
    WHERE measure_id = 10
    GROUP BY time_bucket('1 day'::interval, ts)
)
SELECT
    dt,
    average(tw)
FROM t;

Advanced usage

Parallelism and ordering

Time-weighted average calculations are not strictly parallelizable, as defined by PostgreSQL. These calculations require inputs to be strictly ordered, but in general, PostgreSQL parallelizes by assigning rows randomly to workers.

However, the algorithm can be parallelized if it is guaranteed that all rows within some time range go to the same worker. This is the case for both continuous aggregates and distributed hypertables. (Note that the partitioning keys of the distributed hypertable must be within the GROUP BY clause, but this is usually the case.)

Combining aggregates across measurement series

If you try to combine overlapping TimeWeightSummaries, an error is thrown. For example, you might create a TimeWeightSummary for device_1 and a separate TimeWeightSummary for device_2, both covering the same period of time. You can't combine these because the interpolation techniques only make sense when restricted to a single measurement series.

If you want to calculate a single summary statistic across all devices, use a simple average, like this:


WITH t as (SELECT measure_id,
        average(
            time_weight('LOCF', ts, val)
        ) as time_weighted_average
    FROM foo
    GROUP BY measure_id)
SELECT avg(time_weighted_average) -- use the normal avg function to average the time-weighted averages
FROM t;

Parallelism in multi-node

The time-weighted average functions are not strictly parallelizable in the PostgreSQL sense. PostgreSQL requires that parallelizable functions accept potentially overlapping input. As explained above, the time-weighted functions do not. However, they do support partial aggregation and partition-wise aggregation in multi-node setups.

Reducing memory usage

Because the time-weighted aggregates require ordered sets, they build up a buffer of input data, sort it, and then perform the aggregation steps. When memory is too small to build up a buffer of points, you might see Out of Memory failures or other issues. In these cases, try using a multi-level aggregate. For example:


WITH t as (SELECT measure_id,
    time_bucket('1 day'::interval, ts),
    time_weight('LOCF', ts, val)
    FROM foo
    GROUP BY measure_id, time_bucket('1 day'::interval, ts)
    )
SELECT measure_id,
    average(
        rollup(time_weight)
    )
FROM t
GROUP BY measure_id;

time_weight() functions

Two-step aggregation

Functions in this group

Aggregate

Accessor

Rollup

Function details

time_weight()

average()

first_time()

first_val()

integral()

interpolated_average()

interpolated_integral()

last_time()

last_val()

rollup()

Extended examples

Aggregate data into a `TimeWeightSummary` and calculate the average

Advanced usage

Parallelism and ordering

Combining aggregates across measurement series

Parallelism in multi-node

Reducing memory usage

Introduction

Two-step aggregation

Aggregate

Accessor

Rollup

time_weight()

average()

first_time()

first_val()

integral()

interpolated_average()

interpolated_integral()

last_time()

last_val()

rollup()

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