Predicting millions of independent time series, using them to help each other This is a very general problem faced by different types of companies. Predict future customer behavior over time.
Imagine that we have 1 million customers with their own resources over time, forming a time series. The classic techniques (statistics with ARIMA filters, Bayesian approach as FBprophet or purely computational as LSTM) here is not very suitable, as I would consider that each series is reasonably independent, many series are super sparse or have just started and treated them individually who train a model for each series. So that if we run individual forecasts it would be very bad.
The most conservative approach asks a first classifier to understand what the time series is like (like a grouper species), so we have curves with the same seasonality and trends and then normalize so that the level is the same. We train the models for each of these groups and then go back to the old level and have an individual forecast.
I would like to know if there is a more suitable technique or a canonical solution for the model to understand and predict all series more accurately, using "knowledge of the group" (of the time series that are more similar) in a more scientific and scalable way.
 A: There are two general forecasting techniques I will point you towards.
The first is hierarchical forecasting. This is a good method if you data has a structure where you need to forecast individual series, but also aggregated series (for example forecast each individual item in a store, plus each store's sales). Rob Hyndman has published quite a few papers on this I would point you to this textbook chapter Hierarchical Forecasting - Hyndman (2019), as well as this paper Coherent Probabilistic Forecasts for Hierarchical Time Series - Hyndman (2017). Also along the lines of this is the M5 Forecasting Competition (2020) which took place last year.
The second is vector autoregression with sparsity. It seems from your question that there is some dependence between the time series, but only a small subset of the time series will affect any given series. An example of this can be found in the following paper Sparse Vector Autoregressive Modeling - Davis et. al (2012) or Structured Regularization for Large Vector Autoregressions with Exogenous Variables. In both papers they seek to fit a VAR model where the coefficient matricies are relatively sparse; this is similar to how in standard regression introducing regularization can sometimes improve performance.
A good resource on how to implement these models is the CRAN Task View: Time Series Analysis. As you will be able to see under the heading Multivariate Time Series Models there are a few R packages that can do this type of time series analysis.
A: Could use a Bayesian hierarchical model where each person is a different level.
