Introduction
This vignette provides an overview of key R and Python packages for forecast reconciliation, which follow the FoReco philosophy of providing unified and flexible tools for series forecasting, emphasizing coherence, reproducibility, and a consistent framework across cross-sectional, temporal, and cross-temporal dimensions.
Forecast Reconciliation in R
| Package | Description |
|---|---|
 |
FoReco Classical (bottom-up and top-down), optimal combination and heuristic point (Di Fonzo and Girolimetto, 2023) and probabilistic (Girolimetto et al., 2023) forecast reconciliation procedures for linearly constrained time series (e.g., hierarchical or grouped time series) in cross-sectional, temporal, or cross-temporal frameworks. |
 |
FoCo2 Methods and tools designed to improve forecast accuracy for linearly constrained multiple time series, while fulfilling the linear/aggregation relationships linking the components (Girolimetto and Di Fonzo, 2024). It offers multi-task forecast combination and reconciliation approaches leveraging input from multiple forecasting models or experts and ensuring that the resulting forecasts satisfy specified linear constraints. In addition, linear inequality constraints (e.g., non-negativity of the forecasts) can be imposed, if needed. |
 |
nlcReco Optimal combination forecast reconciliation procedures (Girolimetto et al. 2025) for multiple time series with linear and non-linear constraints in cross-sectional framework. |
Forecast Reconciliation in Python
| Package | Description |
|---|---|
 |
FoRecoPy Optimal combination and heuristic point (Di Fonzo and Girolimetto, 2023) and probabilistic (Girolimetto et al. 2023) forecast reconciliation procedures for linearly constrained time series (e.g., hierarchical or grouped time series) in cross-sectional, temporal, or cross-temporal frameworks, implemented natively in Python. |