Time series: support multiple series
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Beschreibung
**Background**
Sometimes a dataset can contain multiple individual time series trends, where a series identifier column indicates which series each row belongs to. This series ID is part of the input data, and the model can use it to segment the series and learn each individually. If there are relationships or commonalities between the series, the model can ideally take advantage of those relationships.
Example: given individual time series trends across 100 stores, predict next week's sales, for any of those stores.
**Multiseries support**
There's a few different ways to set up this sort of thing:
* General: Provide series ID as another input feature to the model.
* Per-series: build a separate model for each series, and use the series ID to index the corresponding model when making predictions.
We'll have to add the series ID as part of the timeseries problem configuration.
We'll need to consider how to compute objectives for multiseries. My recommendation is to compute the scores per-series and then average the scores across the series. But there are other possibilities.
**Multiseries detrending**
This can interact with seasonality/detrending in a few ways too:
* No seasonality / detrending
* Learn a general trend across all the series, and provide the stationary and non-stationary trends as features to the model
* Learn a general trend across all the series, and model the residual
* Learn a trend for each series, and provide the stationary and non-stationary trends as features to the model
* Learn a trend for each series, and model the residual
**Next Steps**
I think we should do the following:
* To start, implement the "general" strategy from above with no detrending. File the per-series separately as a future item.
* For detrending, prototype the approaches above, measure performance and pick one to implement.
* Add a version of predicted-vs-actual and other timeseries-specific model understanding tooks which can support multiseries.
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