A1297
Title: Cross-temporal probabilistic forecast reconciliation: Methodological and practical issues
Authors: Tommaso Di Fonzo - University of Padova (Italy) [presenting]
Daniele Girolimetto - University of Padova (Italy)
Rob Hyndman - Monash University (Australia)
George Athanasopoulos - Monash University (Australia)
Abstract: Forecast reconciliation is a post-forecasting process that involves transforming a set of incoherent forecasts into coherent forecasts that satisfy a given set of linear constraints for a multivariate time series. The cross-sectional probabilistic forecast reconciliation approach is extended to encompass a cross-temporal framework where temporal constraints are applied. Our proposed methodology employs parametric Gaussian and non-parametric bootstrap approaches to draw samples from an incoherent cross-temporal distribution. The use of multi-step residuals is suggested, especially in the time dimension where the usual one-step residuals fail, present four alternatives for the covariance matrix, where the two-fold nature (cross-sectional and temporal) of the cross-temporal structure is exploited, and the idea of overlapping residuals is introduced. The effectiveness of the proposed cross-temporal reconciliation approaches is assessed through two forecasting experiments using the Australian GDP and the Australian Tourism Demand datasets. The optimal cross-temporal reconciliation approaches for both applications significantly outperform the incoherent base forecasts regarding the Continuous Ranked Probability and Energy Scores.
