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206 lines
12 KiB
Markdown
206 lines
12 KiB
Markdown
---
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slug: /en/sql-reference/aggregate-functions/reference/exponentialmovingaverage
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sidebar_position: 108
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sidebar_title: exponentialMovingAverage
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---
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## exponentialMovingAverage
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Сalculates the exponential moving average of values for the determined time.
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**Syntax**
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```sql
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exponentialMovingAverage(x)(value, timeunit)
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```
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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.
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**Arguments**
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- `value` — Value. [Integer](../../../sql-reference/data-types/int-uint.md), [Float](../../../sql-reference/data-types/float.md) or [Decimal](../../../sql-reference/data-types/decimal.md).
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- `timeunit` — Timeunit. [Integer](../../../sql-reference/data-types/int-uint.md), [Float](../../../sql-reference/data-types/float.md) or [Decimal](../../../sql-reference/data-types/decimal.md). Timeunit is not timestamp (seconds), it's -- an index of the time interval. Can be calculated using [intDiv](../../functions/arithmetic-functions.md#intdiva-b).
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**Parameters**
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- `x` — Half-life period. [Integer](../../../sql-reference/data-types/int-uint.md), [Float](../../../sql-reference/data-types/float.md) or [Decimal](../../../sql-reference/data-types/decimal.md).
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**Returned values**
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- Returnes an [exponentially smoothed moving average](https://en.wikipedia.org/wiki/Moving_average#Exponential_moving_average) of the values for the past `x` time at the latest point of time.
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Type: [Float64](../../../sql-reference/data-types/float.md#float32-float64).
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**Examples**
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Input table:
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``` text
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┌──temperature─┬─timestamp──┐
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│ 95 │ 1 │
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│ 95 │ 2 │
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│ 95 │ 3 │
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│ 96 │ 4 │
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│ 96 │ 5 │
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│ 96 │ 6 │
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│ 96 │ 7 │
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│ 97 │ 8 │
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│ 97 │ 9 │
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│ 97 │ 10 │
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│ 97 │ 11 │
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│ 98 │ 12 │
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│ 98 │ 13 │
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│ 98 │ 14 │
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│ 98 │ 15 │
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│ 99 │ 16 │
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│ 99 │ 17 │
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│ 99 │ 18 │
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│ 100 │ 19 │
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│ 100 │ 20 │
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└──────────────┴────────────┘
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```
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Query:
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```sql
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SELECT exponentialMovingAverage(5)(temperature, timestamp);
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```
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Result:
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``` text
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┌──exponentialMovingAverage(5)(temperature, timestamp)──┐
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│ 92.25779635374204 │
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└───────────────────────────────────────────────────────┘
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```
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Query:
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```sql
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SELECT
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value,
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time,
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round(exp_smooth, 3),
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bar(exp_smooth, 0, 1, 50) AS bar
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FROM
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(
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SELECT
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(number = 0) OR (number >= 25) AS value,
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number AS time,
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exponentialMovingAverage(10)(value, time) OVER (Rows BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW) AS exp_smooth
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FROM numbers(50)
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)
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```
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Result:
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``` text
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┌─value─┬─time─┬─round(exp_smooth, 3)─┬─bar────────────────────────────────────────┐
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│ 1 │ 0 │ 0.067 │ ███▎ │
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│ 0 │ 1 │ 0.062 │ ███ │
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│ 0 │ 2 │ 0.058 │ ██▊ │
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│ 0 │ 3 │ 0.054 │ ██▋ │
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│ 0 │ 4 │ 0.051 │ ██▌ │
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│ 0 │ 5 │ 0.047 │ ██▎ │
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│ 0 │ 6 │ 0.044 │ ██▏ │
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│ 0 │ 7 │ 0.041 │ ██ │
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│ 0 │ 8 │ 0.038 │ █▊ │
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│ 0 │ 9 │ 0.036 │ █▋ │
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│ 0 │ 10 │ 0.033 │ █▋ │
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│ 0 │ 11 │ 0.031 │ █▌ │
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│ 0 │ 12 │ 0.029 │ █▍ │
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│ 0 │ 13 │ 0.027 │ █▎ │
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│ 0 │ 14 │ 0.025 │ █▎ │
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│ 0 │ 15 │ 0.024 │ █▏ │
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│ 0 │ 16 │ 0.022 │ █ │
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│ 0 │ 17 │ 0.021 │ █ │
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│ 0 │ 18 │ 0.019 │ ▊ │
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│ 0 │ 19 │ 0.018 │ ▊ │
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│ 0 │ 20 │ 0.017 │ ▋ │
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│ 0 │ 21 │ 0.016 │ ▋ │
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│ 0 │ 22 │ 0.015 │ ▋ │
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│ 0 │ 23 │ 0.014 │ ▋ │
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│ 0 │ 24 │ 0.013 │ ▋ │
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│ 1 │ 25 │ 0.079 │ ███▊ │
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│ 1 │ 26 │ 0.14 │ ███████ │
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│ 1 │ 27 │ 0.198 │ █████████▊ │
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│ 1 │ 28 │ 0.252 │ ████████████▌ │
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│ 1 │ 29 │ 0.302 │ ███████████████ │
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│ 1 │ 30 │ 0.349 │ █████████████████▍ │
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│ 1 │ 31 │ 0.392 │ ███████████████████▌ │
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│ 1 │ 32 │ 0.433 │ █████████████████████▋ │
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│ 1 │ 33 │ 0.471 │ ███████████████████████▌ │
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│ 1 │ 34 │ 0.506 │ █████████████████████████▎ │
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│ 1 │ 35 │ 0.539 │ ██████████████████████████▊ │
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│ 1 │ 36 │ 0.57 │ ████████████████████████████▌ │
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│ 1 │ 37 │ 0.599 │ █████████████████████████████▊ │
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│ 1 │ 38 │ 0.626 │ ███████████████████████████████▎ │
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│ 1 │ 39 │ 0.651 │ ████████████████████████████████▌ │
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│ 1 │ 40 │ 0.674 │ █████████████████████████████████▋ │
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│ 1 │ 41 │ 0.696 │ ██████████████████████████████████▋ │
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│ 1 │ 42 │ 0.716 │ ███████████████████████████████████▋ │
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│ 1 │ 43 │ 0.735 │ ████████████████████████████████████▋ │
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│ 1 │ 44 │ 0.753 │ █████████████████████████████████████▋ │
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│ 1 │ 45 │ 0.77 │ ██████████████████████████████████████▍ │
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│ 1 │ 46 │ 0.785 │ ███████████████████████████████████████▎ │
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│ 1 │ 47 │ 0.8 │ ███████████████████████████████████████▊ │
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│ 1 │ 48 │ 0.813 │ ████████████████████████████████████████▋ │
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│ 1 │ 49 │ 0.825 │ █████████████████████████████████████████▎│
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└───────┴──────┴──────────────────────┴────────────────────────────────────────────┘
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```
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```sql
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CREATE TABLE data
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ENGINE = Memory AS
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SELECT
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10 AS value,
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toDateTime('2020-01-01') + (3600 * number) AS time
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FROM numbers_mt(10);
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-- Calculate timeunit using intDiv
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SELECT
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value,
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time,
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exponentialMovingAverage(1)(value, intDiv(toUInt32(time), 3600)) OVER (ORDER BY time ASC) AS res,
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intDiv(toUInt32(time), 3600) AS timeunit
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FROM data
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ORDER BY time ASC;
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┌─value─┬────────────────time─┬─────────res─┬─timeunit─┐
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│ 10 │ 2020-01-01 00:00:00 │ 5 │ 438288 │
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│ 10 │ 2020-01-01 01:00:00 │ 7.5 │ 438289 │
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│ 10 │ 2020-01-01 02:00:00 │ 8.75 │ 438290 │
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│ 10 │ 2020-01-01 03:00:00 │ 9.375 │ 438291 │
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│ 10 │ 2020-01-01 04:00:00 │ 9.6875 │ 438292 │
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│ 10 │ 2020-01-01 05:00:00 │ 9.84375 │ 438293 │
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│ 10 │ 2020-01-01 06:00:00 │ 9.921875 │ 438294 │
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│ 10 │ 2020-01-01 07:00:00 │ 9.9609375 │ 438295 │
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│ 10 │ 2020-01-01 08:00:00 │ 9.98046875 │ 438296 │
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│ 10 │ 2020-01-01 09:00:00 │ 9.990234375 │ 438297 │
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└───────┴─────────────────────┴─────────────┴──────────┘
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-- Calculate timeunit using toRelativeHourNum
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SELECT
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value,
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time,
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exponentialMovingAverage(1)(value, toRelativeHourNum(time)) OVER (ORDER BY time ASC) AS res,
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toRelativeHourNum(time) AS timeunit
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FROM data
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ORDER BY time ASC;
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┌─value─┬────────────────time─┬─────────res─┬─timeunit─┐
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│ 10 │ 2020-01-01 00:00:00 │ 5 │ 438288 │
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│ 10 │ 2020-01-01 01:00:00 │ 7.5 │ 438289 │
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│ 10 │ 2020-01-01 02:00:00 │ 8.75 │ 438290 │
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│ 10 │ 2020-01-01 03:00:00 │ 9.375 │ 438291 │
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│ 10 │ 2020-01-01 04:00:00 │ 9.6875 │ 438292 │
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│ 10 │ 2020-01-01 05:00:00 │ 9.84375 │ 438293 │
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│ 10 │ 2020-01-01 06:00:00 │ 9.921875 │ 438294 │
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│ 10 │ 2020-01-01 07:00:00 │ 9.9609375 │ 438295 │
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│ 10 │ 2020-01-01 08:00:00 │ 9.98046875 │ 438296 │
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│ 10 │ 2020-01-01 09:00:00 │ 9.990234375 │ 438297 │
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└───────┴─────────────────────┴─────────────┴──────────┘
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```
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