Fit to national timeseries

[dylanhmorris]

We will also want to consider bottom-up aggregation of state forecasts, but even if/when we find and approach we like, it will be useful to have a national fit as a comparison and/or fallback.

[SamuelBrand1]

@dylanhmorris I think that optimized forecast reconciliation might be worth a test here, in comparison to the optimized copula bottom-up approach we tried last year at points.

Forecast hierarchy

The structure:

• We fit each state/territory (base unit).
• We fit each CDC region (intermediate unit).
• We fit national (top level unit).

We then interleave the forecasts using reconciliation.

Options and resources

• I've been very impressed with fable and the book from the devs https://otexts.com/fpp3/hierarchical.html has a good chapter on this.
• One approach could be to do sample-by-sample minimum trace (MinT) reconciliation. This would involves matching forecast samples across levels (e.g. by .draw), then applying minT to each before re-ensembling. This is equivalent to the Bayesian view of minT forecast across uncertainty in models. Main upside here is that hts package has a function for this with many options, and python versions exist e.g. https://github.com/AngelPone/pyhts
• Another approach is using SGD on the reconciliation using the theory developed here https://www.sciencedirect.com/science/article/abs/pii/S0377221722006087 . This has an associated R repo ProbReco https://github.com/anastasiospanagiotelis/ProbReco but this does not look very functional.

[dylanhmorris]

A basic national timeseries fit is implemented in #102