Using Cross-Temporal Hierarchies to Improve Forecasts from Large Data Sets

• Activity Number: 345 - Advances in Macroeconomic Nowcasting and Forecasting: Role of Traditional and Nontraditional Indicators and Big Data
• Type: Topic-Contributed
• Date/Time: Thursday, August 12, 2021 : 10:00 AM to 11:50 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): Tommaso Di Fonzo* and Daniele Girolimetto
• Companies: University of Padua and University of Padua
• Keywords: Hierarchical forecasting; Cross-temporal reconciliation; M5 dataset

Abstract

We discuss the prediction of hierarchical time series, where each upper series is calculated by summing appropriate lower-level time series. These forecasts should be additively coherent, which means that the forecast for an upper level time series equals the sum of forecasts for the corresponding lower-level time series. The most known methods for making coherent forecasts consist of two phases: first computing base (incoherent) forecasts, and then reconciling those forecasts by exploiting their hierarchical structure. Cross-temporal hierarchies may consistently improve the accuracy of the base forecasts. However, in this case the complexity of the reconciliation becomes very high as the number of series to forecast grows, and calls for appropriate techniques able to deal with such large data structures. We show feasible statistical solutions based on the cross-temporal forecast reconciliation approach (Di Fonzo and Girolimetto, 2020), with an application to the base forecasts of the M5 forecasting competition dataset (Makridakis, Spiliotis and Assimakopoulos, 2020), consisting in 42,840 daily time series of retail sales classified by States, store, category, and department.