ctbu: Cross-temporal bottom-up reconciliation

In FoReco: Forecast Reconciliation

Cross-temporal bottom-up reconciliation

Description

Cross-temporal bottom-up reconciled forecasts for all series at any temporal aggregation level are computed by appropriate summation of the high-frequency bottom base forecasts \widehat{\mathbf{B}}^{[1]}:

\widetilde{\mathbf{X}} = \mathbf{S}_{cs}\widehat{\mathbf{B}}^{[1]}\mathbf{S}'_{te},

where \mathbf{S}_{cs} and \mathbf{S}_{te} are the cross-sectional and temporal structural matrices, respectively.

Usage

ctbu(base, agg_mat, agg_order, tew = "sum", sntz = FALSE, round = FALSE)

Arguments

base	A (n_b \times hm) numeric matrix containing high-frequency bottom base forecasts; n_b is the total number of high-frequency bottom variables, m is the max aggregation order, and h is the forecast horizon for the lowest frequency time series.
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.
agg_order	Highest available sampling frequency per seasonal cycle (max. order of temporal aggregation, m), or a vector representing a subset of p factors of m.
tew	A string specifying the type of temporal aggregation. Options include: "sum" (simple summation, default), "avg" (average), "first" (first value of the period), and "last" (last value of the period).
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 (n \times h(k^\ast+m)) numeric matrix of cross-temporal reconciled forecasts.

References

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: csbu(), tebu()

Cross-temporal framework: ctboot(), ctcov(), ctlcc(), ctmo(), ctmvn(), ctrec(), ctsmp(), cttd(), cttools(), iterec(), tcsrec()

Examples

set.seed(123)
# Aggregation matrix for Z = X + Y
A <- t(c(1,1))
# (2 x 4) high frequency bottom base forecasts matrix (simulated),
# agg_order = 4 (annual-quarterly)
hfbts <- matrix(rnorm(4*2, 2.5), 2, 4)

reco <- ctbu(base = hfbts, agg_mat = A, agg_order = 4)

# Non negative reconciliation
hfbts[1,4] <- -hfbts[1,4] # Making negative one of the quarterly values for X
nnreco <- ctbu(base = hfbts, agg_mat = A, agg_order = 4, sntz = TRUE)

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