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Issue 275: Prototype VARIMA (Analysis - do not merge) #291

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SamuelBrand1
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This draft PR explores the VARIMA baseline model as per #275 and commits an analysis of different VARIMA structures across a few chosen dates with a few chosen ARIMA models aimed at covid and flu NHSN.

This is committed as an analysis here.

Whilst this is not an exhaustive analysis, it shows that the "best" model, as in what time series joint modelling configs have the best out-of-sample CRPS, varies over time and pathogen. This suggests that for multi-signal approaches we probably want to go towards some kind of ensemble over structures to have more consistent forecast performance.

From the pov of a baseline against pyrenew; SARIMA still seems reasonable because it was never the worst time series model.

Linking @seabbs because he was interested in VARIMA.

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codecov bot commented Jan 9, 2025

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 15.87%. Comparing base (9c9d86b) to head (44f3dda).
Report is 5 commits behind head on main.

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##             main     #291      +/-   ##
==========================================
- Coverage   16.54%   15.87%   -0.67%     
==========================================
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  Lines        1481     1537      +56     
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- Hits          245      244       -1     
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Flag Coverage Δ
hewr 47.68% <ø> (-0.11%) ⬇️
pipelines 0.00% <ø> (ø)
pyrenew_hew 1.65% <ø> (-0.24%) ⬇️

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@SamuelBrand1
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Adding a bit of takeaway: In the short term I this analysis plan doesn't give a compelling reason to move away from the current time series baseline (linear pool ensemble of auto-selected ETS + SARIMA univariate ts models) because one of those models is always in the mix of best performing and therefore I don't think gives an "erroneous" baseline to compare the main product pyrenew-h/he to.

However, there are some interesting angles e.g. stacking models that are good in different situation ala stackr.

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VARIMA baseline model for joint forecasting of NSSP and NHSN signals
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