Simultaneous and Two-step Reconciliation of Systems of Time Series

The reconciliation of systems of time series subject to both temporal and contemporaneous constraints can be solved in such a way that the temporal profiles of the original series be preserved "at the best'' (movement preservation principle). Thanks to the sparsity of the linear system to be solved, a feasible procedure can be developed to solve simultaneously the problem. A two-step strategy might be more suitable in the case of large systems: firstly, each series is aligned to the corresponding temporal constraints according to a movement preservation principle; secondly, all series are reconciled within each low-frequency period according to the given constraints. This work compares the results of simultaneous and two-step approaches for medium/large datasets from real-life and discusses conditions under which the two-step procedure can be a valid alternative to the simultaneous one.