Improving forecasts via subspace projections

Date

19 September 2024

Venue

Various

 

Abstract

Univariate, multivariate, and hierarchical forecasts can all be improved using projections onto linear subspaces, regardless of what forecasting method is used. I will show some theoretical guarantees of this statement, and demonstrate using empirical applications how linear projections can lead to (sometimes dramatic) improvements in forecast accuracy.

The procedure involves creating new time series that are linear combinations of the observed time series. These are then forecast, along with the original series, and all forecasts are adjusted via a projection matrix to ensure they satisfy the linear constraints.

This procedure is now widely used for hierarchical forecasting. It has the potential to revolutionise multivariate forecasting as well.

Given at

Slides (Sri Lanka)

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Software

References

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Girolimetto, Daniele, George Athanasopoulos, Tommaso Di Fonzo, and Rob J Hyndman. 2024. “Cross-Temporal Probabilistic Forecast Reconciliation: Methodological and Practical Issues.” International J Forecasting 40 (3): 1134–51. http://robjhyndman.com/publications/ctprob.html.
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Yang, Yangzhuoran Fin, George Athanasopoulos, Rob J Hyndman, and Anastasios Panagiotelis. 2024. “Forecast Linear Augmented Projection (FLAP): A Free Lunch to Reduce Forecast Error Variance.” Working paper. https://robjhyndman.com/publications/flap.html.