Cross-Temporal Forecast Reconciliation: Optimal Combination Method and Heuristic Alternatives

• Activity Number: 161 - Advances in Forecasting of Macroeconomic Variables: New Methods and Applications
• Type: Topic Contributed
• Date/Time: Tuesday, August 4, 2020 : 10:00 AM to 11:50 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): Tommaso Di Fonzo* and Daniele Girolimetto
• Companies: University of Padova and University of Padova
• Keywords: Hierarchical forecasting; Cross-temporal reconciliation; Quarterly Australian GDP; Income and Expenditure sides

Abstract

Forecast reconciliation is a post-forecasting process aimed to improve the quality of the base forecasts for a system of hierarchical/grouped time series (Hyndman et al., 2011). Contemporaneous (cross-sectional) and temporal hierarchies have been considered in the literature, but - except for Kourentzes and Athanasopoulos (2019) - generally these two features have not fully considered together. Adopting a notation able to simultaneously deal with both forecast reconciliation dimensions, the paper shows two new results: (i) an iterative cross-temporal forecast reconciliation procedure, which extends, and overcomes some weaknesses of, the two-step procedure by Kourentzes and Athanasopoulos (2019), and (ii) the closed-form expression of the optimal (in least squares sense) point forecasts which fulfill both contemporaneous and temporal constraints. The feasibility and the performance of the proposed procedures are studied through a forecasting experiment on the 95 quarterly time series of the Australian GDP from Income and Expenditure sides considered by Athanasopoulos et al. (2019).