Game-theoretically Optimal Reconciliation of Contemporaneous Hierarchical Time Series Forecasts

Tim Van Erven 1, 2 Jairo Cugliari 1, 3
1 SELECT - Model selection in statistical learning
Inria Saclay - Ile de France, LMO - Laboratoire de Mathématiques d'Orsay, CNRS - Centre National de la Recherche Scientifique : UMR
Abstract : In hierarchical time series (HTS) forecasting, the hierarchical relation be- tween multiple time series is exploited to make better forecasts. This hierarchical relation implies one or more aggregate consistency constraints that the series are known to satisfy. Many existing approaches, like for example bottom-up or top- down forecasting, therefore attempt to achieve this goal in a way that guarantees that the forecasts will also be aggregate consistent. We propose to split the problem of HTS into two independent steps: first one comes up with the best possible fore- casts for the time series without worrying about aggregate consistency; and then a reconciliation procedure is used to make the forecasts aggregate consistent. We introduce a Game-Theoretically OPtimal (GTOP) reconciliation method, which is guaranteed to only improve any given set of forecasts. This opens up new possibil- ities for constructing the forecasts. For example, it is not necessary to assume that bottom-level forecasts are unbiased, and aggregate forecasts may be constructed by regressing both on bottom-level forecasts and on other covariates that may only be available at the aggregate level. We illustrate the benefits of our approach both on simulated data and on real electricity consumption data.
Type de document :
Pré-publication, Document de travail
2013
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Tim Van Erven, Jairo Cugliari. Game-theoretically Optimal Reconciliation of Contemporaneous Hierarchical Time Series Forecasts. 2013. 〈hal-00920559〉

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