Draft: Regular functions for time series analysis

[LordVoldebug]

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• New Feature

Changelog entry (a user-readable short description of the changes that goes to CHANGELOG.md):

Implementation of several regular functions for time series analysis.

Forecasters:

Signature:

methodName(series, number_to_predict, params, [fill_gaps]) -> Array[values]
methodName(series, times, times_to_predict, params, [fill_gaps]) -> Array[values]

seriesHolt
seriesAdditiveDamped
seriesMultiplicativeDamped
seriesHoltWintersMultiplicative
seriesHoltWintersAdditive
seriesHoltWintersDamped

Stationarity test:

seriesKPSS(series) -> KPSS value

Smoothing functions:

Signature: f(Array) -> Array
seriesEMA
seriesKaufmansAMA

seriesWindowMax
seriesWindowMin
seriesWindowSum
seriesWindowStandardDeviation

Documentation entry for user-facing changes

• Documentation is written (mandatory for new features)

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[rschu1ze]

@LordVoldebug A silly question to begin with ... exponential smoothing needs to "see" the entire time series to produce a forecast (let's leave aside the point that with increasing smoothing factor, historical values become less relevant). Similarly, window-based functions need to see the N last values. Since query processing in ClickHouse is based on chunks and the chunks are processed in random order (not consecutively), how is this problem addressed in this PR?

[LordVoldebug]

@rschu1ze,

@LordVoldebug A silly question to begin with ... exponential smoothing needs to "see" the entire time series to produce a forecast (let's leave aside the point that with increasing smoothing factor, historical values become less relevant). Similarly, window-based functions need to see the N last values. Since query processing in ClickHouse is based on chunks and the chunks are processed in random order (not consecutively), how is this problem addressed in this PR?

This was one of the first questions i faced myself while working on this.

Implemented functions are regular functions which accept arrays; not aggregate functions, and as far as i understood from the codebase and common sense, at the point where we are already given an array the order is fixed (if it is not, there are many functions that would not work...).

And when we need to extract data from the table to an Array, we can use functions like groupArray. In groupArray there is such string in documentation:

https://clickhouse.com/docs/en/sql-reference/aggregate-functions/reference/grouparray

In some cases, you can still rely on the order of execution. This applies to cases when SELECT comes from a subquery that uses ORDER BY if the subquery result is small enough.

So it seems to be ok for most cases. Of course, those functions could have been implemented as aggregate functions, but i thought that the less functions with non strict guarantees, the better.

[rschu1ze]

Okay, that makes sense, thanks. There were similar considerations in earlier PRs that implement time series functions as regular functions, e.g. here and here.

It is still not clear to me what is the best way to implement this. One could argue that "horizontalizing" the data into arrays is an unnecessary step. But that's something to discuss separately, it does not take away from your work (thanks for pushing the PR).

[UnamedRus]

I actually think, that implementing them as window (or aggregate) functions make sense.
As WINDOW definition can have strict guarantees about ordering.
And more importantly, that window definition can be shared across multiple functions. (unlike example with inner implemented ordering like in windowFunnel, so multiple windowFunnel functions will do sorting individually and not efficient. )

BTW

In some cases, you can still rely on the order of execution. This applies to cases when SELECT comes from a subquery that uses ORDER BY if the subquery result is small enough.

Applies for all aggregate functions, not only groupArray.
BTW, there are aggregate functions which internally build array of ts, value and do actual processing only after all data is consumed and sorted windowFunnel for example

Another story, that people wait for different modes of prediction be implemented for ORDER BY xxx WITH FILL INTERPOLATE, which is also interesting option to have (ie, extension of #35349)
Similarish syntax from influxDB

SELECT mean("temperature") FROM "weather_measurement" WHERE "wban" = '00102' group by time(60m) fill(linear)