Enhancements in cross-temporal forecast reconciliation, with an application to solar irradiance forecasts


Tommaso Di Fonzo, Daniele Girolimetto


September 15, 2022

   Publication details

Working paper


In recent works by Yang et al. (2017a,b)12, and Yagli et al. (2019)3, geographical, temporal, and sequential deterministic reconciliation of hierarchical photovoltaic (PV) power generation have been considered for a simulated PV dataset in California. In the first two cases, the reconciliations are carried out in spatial and temporal domains separately. To further improve forecasting accuracy, in the third case these two reconciliation approaches are sequentially applied. During the replication of the forecasting experiment, some issues emerged about non-negativity and coherence (in space and/or in time) of the sequentially reconciled forecasts. Furthermore, while the accuracy improvement of the considered approaches over the benchmark persistence forecasts is clearly visible at any data granularity, we argue that an even better performance may be obtained by a thorough exploitation of cross-temporal hierarchies. In this paper the cross-temporal point forecast reconciliation approach is applied to generate non-negative, fully coherent (both in space and time) forecasts. In particular, some relationships between two-step, iterative and simultaneous cross-temporal reconciliation procedures are for the first time established, non-negativity issues of the final reconciled forecasts are correctly dealt with in a simple way, and the most recent cross-temporal reconciliation approaches are adopted. The normalised Root Mean Square Error is used to measure forecasting accuracy, and a statistical multiple comparison procedure is performed to rank the approaches. Besides assuring full coherence, and non-negativity of the reconciled forecasts, the results show that for the considered dataset, cross-temporal forecast reconciliation significantly improves on the sequential procedures proposed by Yagli et al. (2019), at any cross-sectional level of the hierarchy and for any temporal granularity.

  • 1 Yang, D., Quan, H., Disfani, V.R., Liu, L., 2017a. Reconciling solar forecasts: Geographical hierarchy. Solar Energy 146, 276–286. doi:10.1016/j.solener.2017.02.010.

  • 2 Yang, D., Quan, H., Disfani, V.R., Rodríguez-Gallegos, C.D., 2017b. Reconciling solar forecasts: Temporal hierarchy. Solar Energy 158, 332–346. doi:10.1016/j.solener.2017.09.055.

  • 3 Yagli, G.M., Yang, D., Srinivasan, D., 2019. Reconciling solar forecasts: Sequential reconciliation. Solar Energy 179, 391–397. doi:10.1016/j.solener.2018.12.075.