exponentialMovingAverage
exponentialMovingAverage
Introduced in: v21.11
Calculates the exponential moving average of values for the determined time.
Each value corresponds to the determinate timeunit.
The half-life x is the time lag at which the exponential weights decay by one-half.
The function returns a weighted average: the older the time point, the less weight the corresponding value is considered to be.
Syntax
exponentialMovingAverage(x)(value, timeunit)
Parameters
Arguments
value— Value.(U)Int*orFloat*orDecimaltimeunit— Timeunit. Timeunit is not timestamp (seconds), it's an index of the time interval. Can be calculated usingintDiv.(U)Int*orFloat*orDecimal
Returned value
Returns an exponentially smoothed moving average of the values for the past x time at the latest point of time. Float64
Examples
Basic exponential moving average
-- Input table with temperature data
SELECT exponentialMovingAverage(5)(temperature, timestamp)
FROM VALUES('temperature Int32, timestamp Int32',
(95, 1), (95, 2), (95, 3), (96, 4), (96, 5), (96, 6), (96, 7),
(97, 8), (97, 9), (97, 10), (97, 11), (98, 12), (98, 13), (98, 14),
(98, 15), (99, 16), (99, 17), (99, 18), (100, 19), (100, 20))
┌─exponentialM⋯ timestamp)─┐
│ 92.25779635374204 │
└──────────────────────────┘
Example with the bar function
SELECT
value,
time,
round(exp_smooth, 3),
bar(exp_smooth, 0, 1, 50) AS bar
FROM
(
SELECT
(number = 0) OR (number >= 25) AS value,
number AS time,
exponentialMovingAverage(10)(value, time) OVER (Rows BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW) AS exp_smooth
FROM numbers(50)
)
┌─value─┬─time─┬─round(exp_smooth, 3)─┬─bar────────────────────────────────────────┐
│ 1 │ 0 │ 0.067 │ ███▎ │
│ 0 │ 1 │ 0.062 │ ███ │
│ 0 │ 2 │ 0.058 │ ██▊ │
│ 0 │ 3 │ 0.054 │ ██▋ │
│ 0 │ 4 │ 0.051 │ ██▌ │
│ 0 │ 5 │ 0.047 │ ██▎ │
│ 0 │ 6 │ 0.044 │ ██▏ │
│ 0 │ 7 │ 0.041 │ ██ │
│ 0 │ 8 │ 0.038 │ █▊ │
│ 0 │ 9 │ 0.036 │ █▋ │
│ 0 │ 10 │ 0.033 │ █▋ │
│ 0 │ 11 │ 0.031 │ █▌ │
│ 0 │ 12 │ 0.029 │ █▍ │
│ 0 │ 13 │ 0.027 │ █▎ │
│ 0 │ 14 │ 0.025 │ █▎ │
│ 0 │ 15 │ 0.024 │ █▏ │
│ 0 │ 16 │ 0.022 │ █ │
│ 0 │ 17 │ 0.021 │ █ │
│ 0 │ 18 │ 0.019 │ ▊ │
│ 0 │ 19 │ 0.018 │ ▊ │
│ 0 │ 20 │ 0.017 │ ▋ │
│ 0 │ 21 │ 0.016 │ ▋ │
│ 0 │ 22 │ 0.015 │ ▋ │
│ 0 │ 23 │ 0.014 │ ▋ │
│ 0 │ 24 │ 0.013 │ ▋ │
│ 1 │ 25 │ 0.079 │ ███▊ │
│ 1 │ 26 │ 0.14 │ ███████ │
│ 1 │ 27 │ 0.198 │ █████████▊ │
│ 1 │ 28 │ 0.252 │ ████████████▌ │
│ 1 │ 29 │ 0.302 │ ███████████████ │
│ 1 │ 30 │ 0.349 │ █████████████████▍ │
│ 1 │ 31 │ 0.392 │ ███████████████████▌ │
│ 1 │ 32 │ 0.433 │ █████████████████████▋ │
│ 1 │ 33 │ 0.471 │ ███████████████████████▌ │
│ 1 │ 34 │ 0.506 │ █████████████████████████▎ │
│ 1 │ 35 │ 0.539 │ ██████████████████████████▊ │
│ 1 │ 36 │ 0.57 │ ████████████████████████████▌ │
│ 1 │ 37 │ 0.599 │ █████████████████████████████▊ │
│ 1 │ 38 │ 0.626 │ ███████████████████████████████▎ │
│ 1 │ 39 │ 0.651 │ ████████████████████████████████▌ │
│ 1 │ 40 │ 0.674 │ █████████████████████████████████▋ │
│ 1 │ 41 │ 0.696 │ ██████████████████████████████████▋ │
│ 1 │ 42 │ 0.716 │ ███████████████████████████████████▋ │
│ 1 │ 43 │ 0.735 │ ████████████████████████████████████▋ │
│ 1 │ 44 │ 0.753 │ █████████████████████████████████████▋ │
│ 1 │ 45 │ 0.77 │ ██████████████████████████████████████▍ │
│ 1 │ 46 │ 0.785 │ ███████████████████████████████████████▎ │
│ 1 │ 47 │ 0.8 │ ███████████████████████████████████████▊ │
│ 1 │ 48 │ 0.813 │ ████████████████████████████████████████▋ │
│ 1 │ 49 │ 0.825 │ █████████████████████████████████████████▎ │
└───────┴──────┴──────────────────────┴────────────────────────────────────────────┘
Window function usage with time-based calculation
CREATE TABLE data
ENGINE = Memory AS
SELECT
10 AS value,
toDateTime('2020-01-01') + (3600 * number) AS time
FROM numbers_mt(10);
-- Calculate timeunit using intDiv
SELECT
value,
time,
exponentialMovingAverage(1)(value, intDiv(toUInt32(time), 3600)) OVER (ORDER BY time ASC) AS res,
intDiv(toUInt32(time), 3600) AS timeunit
FROM data
ORDER BY time ASC
┌─value─┬────────────────time─┬─────────res─┬─timeunit─┐
│ 10 │ 2020-01-01 00:00:00 │ 5 │ 438288 │
│ 10 │ 2020-01-01 01:00:00 │ 7.5 │ 438289 │
│ 10 │ 2020-01-01 02:00:00 │ 8.75 │ 438290 │
│ 10 │ 2020-01-01 03:00:00 │ 9.375 │ 438291 │
│ 10 │ 2020-01-01 04:00:00 │ 9.6875 │ 438292 │
│ 10 │ 2020-01-01 05:00:00 │ 9.84375 │ 438293 │
│ 10 │ 2020-01-01 06:00:00 │ 9.921875 │ 438294 │
│ 10 │ 2020-01-01 07:00:00 │ 9.9609375 │ 438295 │
│ 10 │ 2020-01-01 08:00:00 │ 9.98046875 │ 438296 │
│ 10 │ 2020-01-01 09:00:00 │ 9.990234375 │ 438297 │
└───────┴─────────────────────┴─────────────┴──────────┘
