csbu: Cross-sectional bottom-up reconciliation

In FoReco: Forecast Reconciliation

Cross-sectional bottom-up reconciliation

Description

This function computes the cross-sectional bottom-up reconciled forecasts (Dunn et al., 1976) for all series by appropriate summation of the bottom base forecasts \widehat{\mathbf{b}}:

\widetilde{\mathbf{y}} = \mathbf{S}_{cs}\widehat{\mathbf{b}},

where \mathbf{S}_{cs} is the cross-sectional structural matrix.

Usage

csbu(base, agg_mat, sntz = FALSE, round = FALSE)

Arguments

base	A (h \times n_b) numeric matrix or multivariate time series (mts class) containing bottom base forecasts; h is the forecast horizon, and n_b is the total number of bottom variables.
agg_mat	A (n_a \times n_b) numeric matrix representing the cross-sectional aggregation matrix. It maps the n_b bottom-level (free) variables into the n_a upper (constrained) variables.
sntz	Logical. If TRUE, the negative base forecasts are set to zero (Di Fonzo and Girolimetto, 2023) before applying bottom-up. Default is FALSE.
round	Logical. If TRUE, base forecasts are rounded before applying the bottom-up reconciliation. Default is FALSE.

Value

A (h \times n) numeric matrix of cross-sectional reconciled forecasts.

References

Dunn, D. M., Williams, W. H. and Dechaine, T. L. (1976), Aggregate versus subaggregate models in local area forecasting, Journal of the American Statistical Association 71(353), 68–71. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/01621459.1976.10481478")}

Di Fonzo, T. and Girolimetto, D. (2023), Spatio-temporal reconciliation of solar forecasts, Solar Energy, 251, 13–29. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.solener.2023.01.003")}

See Also

Bottom-up reconciliation: ctbu(), tebu()

Cross-sectional framework: csboot(), cscov(), cslcc(), csmo(), csmvn(), csrec(), cssmp(), cstd(), cstools()

Examples

set.seed(123)
# (3 x 2) bottom base forecasts matrix (simulated), Z = X + Y
bts <- matrix(rnorm(6, mean = c(10, 10)), 3, byrow = TRUE)

# Aggregation matrix for Z = X + Y
A <- t(c(1,1))
reco <- csbu(base = bts, agg_mat = A)

# Non negative reconciliation
bts[2,2] <- -bts[2,2] # Making negative one of the base forecasts for Y
nnreco <- csbu(base = bts, agg_mat = A, sntz = TRUE)

FoReco documentation built on March 12, 2026, 5:07 p.m.