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Title: Point and probabilistic forecast reconciliation for general linearly constrained multiple time series Authors:  Tommaso Di Fonzo - University of Padova (Italy) [presenting]
Daniele Girolimetto - University of Padova (Italy)
Abstract: Hierarchical forecast reconciliation is the post-forecasting process aimed at revising a set of incoherent base forecasts into coherent forecasts in line with cross-sectional/temporal/cross-temporal data structure. Most of the point and probabilistic hierarchical forecast reconciliation results move from the classic reconciliation formula valid for the structural representation of a hierarchical time series. When a general linearly constrained multiple time series is considered, the projection approach reconciliation formula gives a general solution. While it is well known that the classic structural reconciliation formula is equivalent to its projection approach counterpart, it is not obvious up to now if and how a structural-like reconciliation formula may be derived for a general, not genuinely hierarchical time series. Such an expression would permit extending definitions, theorems, and results found recently for probabilistic forecast reconciliation in a rather straightforward manner. We show that even for general linearly constrained multiple time series, it is possible to express the reconciliation formula according to a structural approach that keeps distinct free and basic, instead of bottom and upper (aggregated), variables. We extend the definition of probabilistic forecast reconciliation to a general linearly constrained multiple time series, and consider an empirical example.