elastic / elastic/ml-cpp

[ML] Calendar dependent periodic components

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Description

We've had an enhancement request related to a specific sort of cyclical pattern. Specifically, we currently are not able to capture time series behaviour where periodicity is parameterised by calendar features. For example, modulated daily periodicity where the modulation is H,L,H,L,... and H always occurs on the first day of a calendar month.

We could achieve this by, for example, introducing an additive term which is parameterised as periodic(time, calendar feature) to our decompositions. Since we have to keep our models small, we would have to use some sort idea like the one we use to test for the presence of significant calendar components. We would probably also want to limit the number of possible parameterisations we consider. This would all needs some thought.

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